---
_id: '17481'
abstract:
- lang: eng
text: "Phase-field models such as the Allen–Cahn equation may give rise to the formation
and evolution of geometric shapes, a phenomenon that may be analyzed rigorously
in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen–Cahn
equation with a potential with N≥3 distinct minima has been conjectured to describe
the evolution of branched interfaces by multiphase mean curvature flow. In the
present work, we give a rigorous proof for this statement in two and three ambient
dimensions and for a suitable class of potentials: as long as a strong solution
to multiphase mean curvature flow exists, solutions to the vectorial Allen–Cahn
equation with well-prepared initial data converge towards multiphase mean curvature
flow in the limit of vanishing interface width parameter ε↘0. We even establish
the rate of convergence O(ε \r\n1/2\r\n ). Our approach is based on the gradient-flow
structure of the Allen–Cahn equation and its limiting motion: building on the
recent concept of “gradient-flow calibrations” for multiphase mean curvature flow,
we introduce a notion of relative entropy for the vectorial Allen–Cahn equation
with multi-well potential. This enables us to overcome the limitations of other
approaches, e.g. avoiding the need for a stability analysis of the Allen–Cahn
operator or additional convergence hypotheses for the energy at positive times."
acknowledgement: "The authors thank Sebastian Hensel for useful and helpful commentson
the first draft of this work.\r\nThis project has received funding from the European
Research Council (ERC)\r\nunder the European Union’s Horizon 2020 research and innovation
programme (grant\r\nagreement no. 948819."
article_processing_charge: Yes
article_type: original
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen–Cahn
equation towards multiphase mean curvature flow. Annales de l’Institut Henri
Poincare C. 2024;41(5):1117-1178. doi:10.4171/AIHPC/109
apa: Fischer, J. L., & Marveggio, A. (2024). Quantitative convergence of the
vectorial Allen–Cahn equation towards multiphase mean curvature flow. Annales
de l’Institut Henri Poincare C. EMS Press. https://doi.org/10.4171/AIHPC/109
chicago: Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the
Vectorial Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales
de l’Institut Henri Poincare C. EMS Press, 2024. https://doi.org/10.4171/AIHPC/109.
ieee: J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial
Allen–Cahn equation towards multiphase mean curvature flow,” Annales de l’Institut
Henri Poincare C, vol. 41, no. 5. EMS Press, pp. 1117–1178, 2024.
ista: Fischer JL, Marveggio A. 2024. Quantitative convergence of the vectorial Allen–Cahn
equation towards multiphase mean curvature flow. Annales de l’Institut Henri Poincare
C. 41(5), 1117–1178.
mla: Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial
Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales de l’Institut
Henri Poincare C, vol. 41, no. 5, EMS Press, 2024, pp. 1117–78, doi:10.4171/AIHPC/109.
short: J.L. Fischer, A. Marveggio, Annales de l’Institut Henri Poincare C 41 (2024)
1117–1178.
corr_author: '1'
date_created: 2024-09-01T22:01:09Z
date_published: 2024-01-24T00:00:00Z
date_updated: 2025-09-08T09:11:01Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.4171/AIHPC/109
ec_funded: 1
external_id:
isi:
- '001293853900003'
file:
- access_level: open_access
checksum: b5ad02d9abd5b4701269cd1ad0a1cc8f
content_type: application/pdf
creator: dernst
date_created: 2024-09-09T07:46:42Z
date_updated: 2024-09-09T07:46:42Z
file_id: '17923'
file_name: 2024_AnnInstHPoincare_Fischer.pdf
file_size: 1348896
relation: main_file
success: 1
file_date_updated: 2024-09-09T07:46:42Z
has_accepted_license: '1'
intvolume: ' 41'
isi: 1
issue: '5'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 1117-1178
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Annales de l'Institut Henri Poincare C
publication_identifier:
eissn:
- 1873-1430
issn:
- 0294-1449
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '14597'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase
mean curvature flow
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 41
year: '2024'
...
---
_id: '14042'
abstract:
- lang: eng
text: Long-time and large-data existence of weak solutions for initial- and boundary-value
problems concerning three-dimensional flows of incompressible fluids is nowadays
available not only for Navier–Stokes fluids but also for various fluid models
where the relation between the Cauchy stress tensor and the symmetric part of
the velocity gradient is nonlinear. The majority of such studies however concerns
models where such a dependence is explicit (the stress is a function of the velocity
gradient), which makes the class of studied models unduly restrictive. The same
concerns boundary conditions, or more precisely the slipping mechanisms on the
boundary, where the no-slip is still the most preferred condition considered in
the literature. Our main objective is to develop a robust mathematical theory
for unsteady internal flows of implicitly constituted incompressible fluids with
implicit relations between the tangential projections of the velocity and the
normal traction on the boundary. The theory covers numerous rheological models
used in chemistry, biorheology, polymer and food industry as well as in geomechanics.
It also includes, as special cases, nonlinear slip as well as stick–slip boundary
conditions. Unlike earlier studies, the conditions characterizing admissible classes
of constitutive equations are expressed by means of tools of elementary calculus.
In addition, a fully constructive proof (approximation scheme) is incorporated.
Finally, we focus on the question of uniqueness of such weak solutions.
acknowledgement: "M. Bulíček and J. Málek acknowledge the support of the project No.
20-11027X financed by the Czech Science foundation (GAČR). M. Bulíček and J. Málek
are members of the Nečas Center for Mathematical Modelling.\r\nOpen access publishing
supported by the National Technical Library in Prague."
article_number: '72'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Miroslav
full_name: Bulíček, Miroslav
last_name: Bulíček
- first_name: Josef
full_name: Málek, Josef
last_name: Málek
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
citation:
ama: Bulíček M, Málek J, Maringová E. On unsteady internal flows of incompressible
fluids characterized by implicit constitutive equations in the bulk and on the
boundary. Journal of Mathematical Fluid Mechanics. 2023;25(3). doi:10.1007/s00021-023-00803-w
apa: Bulíček, M., Málek, J., & Maringová, E. (2023). On unsteady internal flows
of incompressible fluids characterized by implicit constitutive equations in the
bulk and on the boundary. Journal of Mathematical Fluid Mechanics. Springer
Nature. https://doi.org/10.1007/s00021-023-00803-w
chicago: Bulíček, Miroslav, Josef Málek, and Erika Maringová. “On Unsteady Internal
Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations
in the Bulk and on the Boundary.” Journal of Mathematical Fluid Mechanics.
Springer Nature, 2023. https://doi.org/10.1007/s00021-023-00803-w.
ieee: M. Bulíček, J. Málek, and E. Maringová, “On unsteady internal flows of incompressible
fluids characterized by implicit constitutive equations in the bulk and on the
boundary,” Journal of Mathematical Fluid Mechanics, vol. 25, no. 3. Springer
Nature, 2023.
ista: Bulíček M, Málek J, Maringová E. 2023. On unsteady internal flows of incompressible
fluids characterized by implicit constitutive equations in the bulk and on the
boundary. Journal of Mathematical Fluid Mechanics. 25(3), 72.
mla: Bulíček, Miroslav, et al. “On Unsteady Internal Flows of Incompressible Fluids
Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary.”
Journal of Mathematical Fluid Mechanics, vol. 25, no. 3, 72, Springer Nature,
2023, doi:10.1007/s00021-023-00803-w.
short: M. Bulíček, J. Málek, E. Maringová, Journal of Mathematical Fluid Mechanics
25 (2023).
date_created: 2023-08-13T22:01:13Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-12-13T12:08:08Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00021-023-00803-w
external_id:
arxiv:
- '2301.12834'
isi:
- '001040354900001'
file:
- access_level: open_access
checksum: c549cd8f0dd02ed60477a05ca045f481
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T07:24:17Z
date_updated: 2023-08-14T07:24:17Z
file_id: '14046'
file_name: 2023_JourMathFluidMech_Bulicek.pdf
file_size: 845748
relation: main_file
success: 1
file_date_updated: 2023-08-14T07:24:17Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '3'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
publication: Journal of Mathematical Fluid Mechanics
publication_identifier:
eissn:
- 1422-6952
issn:
- 1422-6928
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On unsteady internal flows of incompressible fluids characterized by implicit
constitutive equations in the bulk and on the boundary
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2023'
...
---
_id: '14554'
abstract:
- lang: eng
text: 'The Regularised Inertial Dean–Kawasaki model (RIDK) – introduced by the authors
and J. Zimmer in earlier works – is a nonlinear stochastic PDE capturing fluctuations
around the meanfield limit for large-scale particle systems in both particle density
and momentum density. We focus on the following two aspects. Firstly, we set up
a Discontinuous Galerkin (DG) discretisation scheme for the RIDK model: we provide
suitable definitions of numerical fluxes at the interface of the mesh elements
which are consistent with the wave-type nature of the RIDK model and grant stability
of the simulations, and we quantify the rate of convergence in mean square to
the continuous RIDK model. Secondly, we introduce modifications of the RIDK model
in order to preserve positivity of the density (such a feature only holds in a
“high-probability sense” for the original RIDK model). By means of numerical simulations,
we show that the modifications lead to physically realistic and positive density
profiles. In one case, subject to additional regularity constraints, we also prove
positivity. Finally, we present an application of our methodology to a system
of diffusing and reacting particles. Our Python code is available in open-source
format.'
acknowledgement: "The authors thank the anonymous referees for their careful reading
of the manuscript and their\r\nvaluable suggestions. FC gratefully acknowledges
funding from the Austrian Science Fund (FWF) through the project F65, and from the
European Union’s Horizon 2020 research and innovation programme under the Marie
Sk lodowska-Curie grant agreement No. 754411 (the latter funding source covered
the first part of this project)."
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
citation:
ama: 'Cornalba F, Shardlow T. The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM:
Mathematical Modelling and Numerical Analysis. 2023;57(5):3061-3090. doi:10.1051/m2an/2023077'
apa: 'Cornalba, F., & Shardlow, T. (2023). The regularised inertial Dean’ Kawasaki
equation: Discontinuous Galerkin approximation and modelling for low-density regime.
ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences. https://doi.org/10.1051/m2an/2023077'
chicago: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’
Kawasaki Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density
Regime.” ESAIM: Mathematical Modelling and Numerical Analysis. EDP Sciences,
2023. https://doi.org/10.1051/m2an/2023077.'
ieee: 'F. Cornalba and T. Shardlow, “The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime,” ESAIM:
Mathematical Modelling and Numerical Analysis, vol. 57, no. 5. EDP Sciences,
pp. 3061–3090, 2023.'
ista: 'Cornalba F, Shardlow T. 2023. The regularised inertial Dean’ Kawasaki equation:
Discontinuous Galerkin approximation and modelling for low-density regime. ESAIM:
Mathematical Modelling and Numerical Analysis. 57(5), 3061–3090.'
mla: 'Cornalba, Federico, and Tony Shardlow. “The Regularised Inertial Dean’ Kawasaki
Equation: Discontinuous Galerkin Approximation and Modelling for Low-Density Regime.”
ESAIM: Mathematical Modelling and Numerical Analysis, vol. 57, no. 5, EDP
Sciences, 2023, pp. 3061–90, doi:10.1051/m2an/2023077.'
short: 'F. Cornalba, T. Shardlow, ESAIM: Mathematical Modelling and Numerical Analysis
57 (2023) 3061–3090.'
corr_author: '1'
date_created: 2023-11-19T23:00:55Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2025-09-09T13:21:05Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1051/m2an/2023077
ec_funded: 1
external_id:
isi:
- '001087237700001'
file:
- access_level: open_access
checksum: 3aef1475b1882c8dec112df9a5167c39
content_type: application/pdf
creator: dernst
date_created: 2023-11-20T08:34:57Z
date_updated: 2023-11-20T08:34:57Z
file_id: '14560'
file_name: 2023_ESAIM_Cornalba.pdf
file_size: 1508534
relation: main_file
success: 1
file_date_updated: 2023-11-20T08:34:57Z
has_accepted_license: '1'
intvolume: ' 57'
isi: 1
issue: '5'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 3061-3090
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: 'ESAIM: Mathematical Modelling and Numerical Analysis'
publication_identifier:
eissn:
- 2804-7214
issn:
- 2822-7840
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
related_material:
link:
- relation: software
url: https://github.com/tonyshardlow/RIDK-FD
scopus_import: '1'
status: public
title: 'The regularised inertial Dean'' Kawasaki equation: Discontinuous Galerkin
approximation and modelling for low-density regime'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 57
year: '2023'
...
---
_id: '14661'
abstract:
- lang: eng
text: 'This paper is concerned with equilibrium configurations of one-dimensional
particle systems with non-convex nearest-neighbour and next-to-nearest-neighbour
interactions and its passage to the continuum. The goal is to derive compactness
results for a Γ-development of the energy with the novelty that external forces
are allowed. In particular, the forces may depend on Lagrangian or Eulerian coordinates
and thus may model dead as well as live loads. Our result is based on a new technique
for deriving compactness results which are required for calculating the first-order
Γ-limit in the presence of external forces: instead of comparing a configuration
of n atoms to a global minimizer of the Γ-limit, we compare the configuration
to a minimizer in some subclass of functions which in some sense are "close to"
the configuration. The paper is complemented with the study of the minimizers
of the Γ-limit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Marcello
full_name: Carioni, Marcello
last_name: Carioni
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Anja
full_name: Schlömerkemper, Anja
last_name: Schlömerkemper
citation:
ama: 'Carioni M, Fischer JL, Schlömerkemper A. External forces in the continuum
limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development. Journal of Convex Analysis. 2023;30(1):217-247.'
apa: 'Carioni, M., Fischer, J. L., & Schlömerkemper, A. (2023). External forces
in the continuum limit of discrete systems with non-convex interaction potentials:
Compactness for a Γ-development. Journal of Convex Analysis. Heldermann
Verlag.'
chicago: 'Carioni, Marcello, Julian L Fischer, and Anja Schlömerkemper. “External
Forces in the Continuum Limit of Discrete Systems with Non-Convex Interaction
Potentials: Compactness for a Γ-Development.” Journal of Convex Analysis.
Heldermann Verlag, 2023.'
ieee: 'M. Carioni, J. L. Fischer, and A. Schlömerkemper, “External forces in the
continuum limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development,” Journal of Convex Analysis, vol. 30, no. 1. Heldermann
Verlag, pp. 217–247, 2023.'
ista: 'Carioni M, Fischer JL, Schlömerkemper A. 2023. External forces in the continuum
limit of discrete systems with non-convex interaction potentials: Compactness
for a Γ-development. Journal of Convex Analysis. 30(1), 217–247.'
mla: 'Carioni, Marcello, et al. “External Forces in the Continuum Limit of Discrete
Systems with Non-Convex Interaction Potentials: Compactness for a Γ-Development.”
Journal of Convex Analysis, vol. 30, no. 1, Heldermann Verlag, 2023, pp.
217–47.'
short: M. Carioni, J.L. Fischer, A. Schlömerkemper, Journal of Convex Analysis 30
(2023) 217–247.
corr_author: '1'
date_created: 2023-12-10T23:00:59Z
date_published: 2023-01-01T00:00:00Z
date_updated: 2024-10-09T21:07:35Z
day: '01'
department:
- _id: JuFi
external_id:
arxiv:
- '1811.09857'
isi:
- '001115503400013'
intvolume: ' 30'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1811.09857
month: '01'
oa: 1
oa_version: Preprint
page: 217-247
publication: Journal of Convex Analysis
publication_identifier:
eissn:
- 2363-6394
issn:
- 0944-6532
publication_status: published
publisher: Heldermann Verlag
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'External forces in the continuum limit of discrete systems with non-convex
interaction potentials: Compactness for a Γ-development'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 30
year: '2023'
...
---
_id: '12429'
abstract:
- lang: eng
text: In this paper, we consider traces at initial times for functions with mixed
time-space smoothness. Such results are often needed in the theory of evolution
equations. Our result extends and unifies many previous results. Our main improvement
is that we can allow general interpolation couples. The abstract results are applied
to regularity problems for fractional evolution equations and stochastic evolution
equations, where uniform trace estimates on the half-line are shown.
acknowledgement: The first author has been partially supported by the Nachwuchsring—Network
for the promotion of young scientists—at TU Kaiserslautern. The second and third
authors were supported by the Vidi subsidy 639.032.427 of the Netherlands Organisation
for Scientific Research (NWO).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Nick
full_name: Lindemulder, Nick
last_name: Lindemulder
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications
to evolution equations. Mathematische Nachrichten. 2023;296(4):1319-1350.
doi:10.1002/mana.202100192
apa: Agresti, A., Lindemulder, N., & Veraar, M. (2023). On the trace embedding
and its applications to evolution equations. Mathematische Nachrichten.
Wiley. https://doi.org/10.1002/mana.202100192
chicago: Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding
and Its Applications to Evolution Equations.” Mathematische Nachrichten.
Wiley, 2023. https://doi.org/10.1002/mana.202100192.
ieee: A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its
applications to evolution equations,” Mathematische Nachrichten, vol. 296,
no. 4. Wiley, pp. 1319–1350, 2023.
ista: Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications
to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.
mla: Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution
Equations.” Mathematische Nachrichten, vol. 296, no. 4, Wiley, 2023, pp.
1319–50, doi:10.1002/mana.202100192.
short: A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023)
1319–1350.
date_created: 2023-01-29T23:00:59Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-16T11:41:42Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1002/mana.202100192
external_id:
arxiv:
- '2104.05063'
isi:
- '000914134900001'
file:
- access_level: open_access
checksum: 6f099f1d064173784d1a27716a2cc795
content_type: application/pdf
creator: dernst
date_created: 2023-08-16T11:40:02Z
date_updated: 2023-08-16T11:40:02Z
file_id: '14067'
file_name: 2023_MathNachrichten_Agresti.pdf
file_size: 449280
relation: main_file
success: 1
file_date_updated: 2023-08-16T11:40:02Z
has_accepted_license: '1'
intvolume: ' 296'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 1319-1350
publication: Mathematische Nachrichten
publication_identifier:
eissn:
- 1522-2616
issn:
- 0025-584X
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the trace embedding and its applications to evolution equations
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 296
year: '2023'
...
---
_id: '13043'
abstract:
- lang: eng
text: "We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction\r\nof a gradient flow calibration in the sense
of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends
the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting
along triple junctions."
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement no. 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
citation:
ama: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484
apa: Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature
flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023.
https://doi.org/10.4171/IFB/484.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS
Press, pp. 37–107, 2023.
ista: Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow
of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1,
EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.
short: S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.
corr_author: '1'
date_created: 2023-05-21T22:01:06Z
date_published: 2023-04-20T00:00:00Z
date_updated: 2025-04-14T09:35:57Z
day: '20'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.4171/IFB/484
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
isi:
- '000975817300002'
file:
- access_level: open_access
checksum: 622422484810441e48f613e968c7e7a4
content_type: application/pdf
creator: dernst
date_created: 2023-05-22T07:24:13Z
date_updated: 2023-05-22T07:24:13Z
file_id: '13045'
file_name: 2023_Interfaces_Hensel.pdf
file_size: 867876
relation: main_file
success: 1
file_date_updated: 2023-05-22T07:24:13Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '1'
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 37-107
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Interfaces and Free Boundaries
publication_identifier:
eissn:
- 1463-9971
issn:
- 1463-9963
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
record:
- id: '10013'
relation: earlier_version
status: public
scopus_import: '1'
status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2023'
...
---
_id: '13135'
abstract:
- lang: eng
text: In this paper we consider a class of stochastic reaction-diffusion equations.
We provide local well-posedness, regularity, blow-up criteria and positivity of
solutions. The key novelties of this work are related to the use transport noise,
critical spaces and the proof of higher order regularity of solutions – even in
case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity
estimates and sharp blow-up criteria. We view the results of this paper as a general
toolbox for establishing global well-posedness for a large class of reaction-diffusion
systems of practical interest, of which many are completely open. In our follow-up
work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra
equations and the Brusselator model.
acknowledgement: The first author has received funding from the European Research
Council (ERC) under the European Union's Horizon 2020 research and innovation programme
(grant agreement No. 948819) Image 1. The second author is supported by the VICI
subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: Yes (in subscription journal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: 'Agresti A, Veraar M. Reaction-diffusion equations with transport noise and
critical superlinear diffusion: Local well-posedness and positivity. Journal
of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038'
apa: 'Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport
noise and critical superlinear diffusion: Local well-posedness and positivity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038'
chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.'
ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity,” Journal
of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.'
ista: 'Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity. Journal
of Differential Equations. 368(9), 247–300.'
mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport
Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp.
247–300, doi:10.1016/j.jde.2023.05.038.'
short: A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.
corr_author: '1'
date_created: 2023-06-18T22:00:45Z
date_published: 2023-09-25T00:00:00Z
date_updated: 2025-04-14T07:53:59Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2023.05.038
ec_funded: 1
external_id:
isi:
- '001019018700001'
file:
- access_level: open_access
checksum: 246b703b091dfe047bfc79abf0891a63
content_type: application/pdf
creator: dernst
date_created: 2024-01-29T11:03:09Z
date_updated: 2024-01-29T11:03:09Z
file_id: '14895'
file_name: 2023_JourDifferentialEquations_Agresti.pdf
file_size: 834638
relation: main_file
success: 1
file_date_updated: 2024-01-29T11:03:09Z
has_accepted_license: '1'
intvolume: ' 368'
isi: 1
issue: '9'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 247-300
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Reaction-diffusion equations with transport noise and critical superlinear
diffusion: Local well-posedness and positivity'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 368
year: '2023'
...
---
_id: '14755'
abstract:
- lang: eng
text: We consider the sharp interface limit for the scalar-valued and vector-valued
Allen–Cahn equation with homogeneous Neumann boundary condition in a bounded smooth
domain Ω of arbitrary dimension N ⩾ 2 in the situation when a two-phase diffuse
interface has developed and intersects the boundary ∂ Ω. The limit problem is
mean curvature flow with 90°-contact angle and we show convergence in strong norms
for well-prepared initial data as long as a smooth solution to the limit problem
exists. To this end we assume that the limit problem has a smooth solution on
[ 0 , T ] for some time T > 0. Based on the latter we construct suitable curvilinear
coordinates and set up an asymptotic expansion for the scalar-valued and the vector-valued
Allen–Cahn equation. In order to estimate the difference of the exact and approximate
solutions with a Gronwall-type argument, a spectral estimate for the linearized
Allen–Cahn operator in both cases is required. The latter will be shown in a separate
paper, cf. (Moser (2021)).
acknowledgement: "The author gratefully acknowledges support through DFG, GRK 1692
“Curvature,\r\nCycles and Cohomology” during parts of the work."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: 'Moser M. Convergence of the scalar- and vector-valued Allen–Cahn equation
to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence
result. Asymptotic Analysis. 2023;131(3-4):297-383. doi:10.3233/asy-221775'
apa: 'Moser, M. (2023). Convergence of the scalar- and vector-valued Allen–Cahn
equation to mean curvature flow with 90°-contact angle in higher dimensions, part
I: Convergence result. Asymptotic Analysis. IOS Press. https://doi.org/10.3233/asy-221775'
chicago: 'Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn
Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part
I: Convergence Result.” Asymptotic Analysis. IOS Press, 2023. https://doi.org/10.3233/asy-221775.'
ieee: 'M. Moser, “Convergence of the scalar- and vector-valued Allen–Cahn equation
to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence
result,” Asymptotic Analysis, vol. 131, no. 3–4. IOS Press, pp. 297–383,
2023.'
ista: 'Moser M. 2023. Convergence of the scalar- and vector-valued Allen–Cahn equation
to mean curvature flow with 90°-contact angle in higher dimensions, part I: Convergence
result. Asymptotic Analysis. 131(3–4), 297–383.'
mla: 'Moser, Maximilian. “Convergence of the Scalar- and Vector-Valued Allen–Cahn
Equation to Mean Curvature Flow with 90°-Contact Angle in Higher Dimensions, Part
I: Convergence Result.” Asymptotic Analysis, vol. 131, no. 3–4, IOS Press,
2023, pp. 297–383, doi:10.3233/asy-221775.'
short: M. Moser, Asymptotic Analysis 131 (2023) 297–383.
corr_author: '1'
date_created: 2024-01-08T13:13:28Z
date_published: 2023-02-02T00:00:00Z
date_updated: 2025-09-09T14:14:55Z
day: '02'
department:
- _id: JuFi
doi: 10.3233/asy-221775
external_id:
arxiv:
- '2105.07100'
isi:
- '000927801300001'
intvolume: ' 131'
isi: 1
issue: 3-4
keyword:
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.07100
month: '02'
oa: 1
oa_version: Preprint
page: 297-383
publication: Asymptotic Analysis
publication_identifier:
eissn:
- 1875-8576
issn:
- 0921-7134
publication_status: published
publisher: IOS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence of the scalar- and vector-valued Allen–Cahn equation to mean curvature
flow with 90°-contact angle in higher dimensions, part I: Convergence result'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 131
year: '2023'
...
---
_id: '14772'
abstract:
- lang: eng
text: "Many coupled evolution equations can be described via 2×2-block operator
matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with
possibly unbounded entries. Here, the case of diagonally dominant block operator
matrices is considered, that is, the case where the full operator A can be seen
as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D)
though with possibly large relative bound. For such operators the properties of
sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied,
and for these properties perturbation results for possibly large but structured
perturbations are derived. Thereby, the time dependent parabolic problem associated
with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied
to a wide range of problems such as different theories for liquid crystals, an
artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel
model."
acknowledgement: "We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for
valuable discussions. We also thank the anonymous referees for their helpful comments
and suggestions, and for the very accurate reading of the manuscript.\r\nThe first
author has been supported partially by the Nachwuchsring – Network for the promotion
of young scientists – at TU Kaiserslautern. Both authors have been supported by
MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative
of the Federal State of Rhineland-Palatinate, Germany."
article_number: '110146'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Amru
full_name: Hussein, Amru
last_name: Hussein
citation:
ama: Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator
matrices and applications. Journal of Functional Analysis. 2023;285(11).
doi:10.1016/j.jfa.2023.110146
apa: Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus
for block operator matrices and applications. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2023.110146
chicago: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis.
Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146.
ieee: A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications,” Journal of Functional Analysis, vol.
285, no. 11. Elsevier, 2023.
ista: Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.
mla: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis,
vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146.
short: A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).
corr_author: '1'
date_created: 2024-01-10T09:15:18Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-10-09T21:07:48Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jfa.2023.110146
external_id:
arxiv:
- '2108.01962'
isi:
- '001081809000001'
file:
- access_level: open_access
checksum: eda98ca2aa73da91bd074baed34c2b3c
content_type: application/pdf
creator: dernst
date_created: 2024-01-10T11:23:57Z
date_updated: 2024-01-10T11:23:57Z
file_id: '14789'
file_name: 2023_JourFunctionalAnalysis_Agresti.pdf
file_size: 1120592
relation: main_file
success: 1
file_date_updated: 2024-01-10T11:23:57Z
has_accepted_license: '1'
intvolume: ' 285'
isi: 1
issue: '11'
keyword:
- Analysis
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximal Lp-regularity and H∞-calculus for block operator matrices and applications
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 285
year: '2023'
...
---
_id: '10173'
abstract:
- lang: eng
text: We study the large scale behavior of elliptic systems with stationary random
coefficient that have only slowly decaying correlations. To this aim we analyze
the so-called corrector equation, a degenerate elliptic equation posed in the
probability space. In this contribution, we use a parabolic approach and optimally
quantify the time decay of the semigroup. For the theoretical point of view, we
prove an optimal decay estimate of the gradient and flux of the corrector when
spatially averaged over a scale R larger than 1. For the numerical point of view,
our results provide convenient tools for the analysis of various numerical methods.
acknowledgement: "I would like to thank my advisor Antoine Gloria for suggesting this
problem to me, as well for many interesting discussions and suggestions.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
citation:
ama: 'Clozeau N. Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields. Stochastics and Partial Differential Equations:
Analysis and Computations. 2023;11:1254–1378. doi:10.1007/s40072-022-00254-w'
apa: 'Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic
homogenization for correlated coefficient fields. Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-022-00254-w'
chicago: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic
Homogenization for Correlated Coefficient Fields.” Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature, 2023.
https://doi.org/10.1007/s40072-022-00254-w.'
ieee: 'N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields,” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 11. Springer Nature, pp. 1254–1378, 2023.'
ista: 'Clozeau N. 2023. Optimal decay of the parabolic semigroup in stochastic homogenization
for correlated coefficient fields. Stochastics and Partial Differential Equations:
Analysis and Computations. 11, 1254–1378.'
mla: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic
Homogenization for Correlated Coefficient Fields.” Stochastics and Partial
Differential Equations: Analysis and Computations, vol. 11, Springer Nature,
2023, pp. 1254–1378, doi:10.1007/s40072-022-00254-w.'
short: 'N. Clozeau, Stochastics and Partial Differential Equations: Analysis and
Computations 11 (2023) 1254–1378.'
corr_author: '1'
date_created: 2021-10-23T10:50:22Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2024-10-09T21:01:04Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-022-00254-w
external_id:
arxiv:
- '2102.07452'
isi:
- '000799715600001'
file:
- access_level: open_access
checksum: f83dcaecdbd3ace862c4ed97a20e8501
content_type: application/pdf
creator: dernst
date_created: 2023-08-14T11:51:04Z
date_updated: 2023-08-14T11:51:04Z
file_id: '14052'
file_name: 2023_StochPartialDiffEquations_Clozeau.pdf
file_size: 1635193
relation: main_file
success: 1
file_date_updated: 2023-08-14T11:51:04Z
has_accepted_license: '1'
intvolume: ' 11'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1254–1378
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Optimal decay of the parabolic semigroup in stochastic homogenization for
correlated coefficient fields
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 11
year: '2023'
...
---
_id: '10550'
abstract:
- lang: eng
text: The global existence of renormalised solutions and convergence to equilibrium
for reaction-diffusion systems with non-linear diffusion are investigated. The
system is assumed to have quasi-positive non-linearities and to satisfy an entropy
inequality. The difficulties in establishing global renormalised solutions caused
by possibly degenerate diffusion are overcome by introducing a new class of weighted
truncation functions. By means of the obtained global renormalised solutions,
we study the large-time behaviour of complex balanced systems arising from chemical
reaction network theory with non-linear diffusion. When the reaction network does
not admit boundary equilibria, the complex balanced equilibrium is shown, by using
the entropy method, to exponentially attract all renormalised solutions in the
same compatibility class. This convergence extends even to a range of non-linear
diffusion, where global existence is an open problem, yet we are able to show
that solutions to approximate systems converge exponentially to equilibrium uniformly
in the regularisation parameter.
acknowledgement: "We thank the referees for their valuable comments and suggestions.
A major part of this work was carried out when B. Q. Tang visited the Institute
of Science and Technology Austria (ISTA). The hospitality of ISTA is greatly acknowledged.
This work was partially supported by NAWI Graz.\r\nOpen access funding provided
by University of Graz."
article_number: '66'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Klemens
full_name: Fellner, Klemens
last_name: Fellner
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
- first_name: Bao Quoc
full_name: Tang, Bao Quoc
last_name: Tang
citation:
ama: Fellner K, Fischer JL, Kniely M, Tang BQ. Global renormalised solutions and
equilibration of reaction-diffusion systems with non-linear diffusion. Journal
of Nonlinear Science. 2023;33. doi:10.1007/s00332-023-09926-w
apa: Fellner, K., Fischer, J. L., Kniely, M., & Tang, B. Q. (2023). Global renormalised
solutions and equilibration of reaction-diffusion systems with non-linear diffusion.
Journal of Nonlinear Science. Springer Nature. https://doi.org/10.1007/s00332-023-09926-w
chicago: Fellner, Klemens, Julian L Fischer, Michael Kniely, and Bao Quoc Tang.
“Global Renormalised Solutions and Equilibration of Reaction-Diffusion Systems
with Non-Linear Diffusion.” Journal of Nonlinear Science. Springer Nature,
2023. https://doi.org/10.1007/s00332-023-09926-w.
ieee: K. Fellner, J. L. Fischer, M. Kniely, and B. Q. Tang, “Global renormalised
solutions and equilibration of reaction-diffusion systems with non-linear diffusion,”
Journal of Nonlinear Science, vol. 33. Springer Nature, 2023.
ista: Fellner K, Fischer JL, Kniely M, Tang BQ. 2023. Global renormalised solutions
and equilibration of reaction-diffusion systems with non-linear diffusion. Journal
of Nonlinear Science. 33, 66.
mla: Fellner, Klemens, et al. “Global Renormalised Solutions and Equilibration of
Reaction-Diffusion Systems with Non-Linear Diffusion.” Journal of Nonlinear
Science, vol. 33, 66, Springer Nature, 2023, doi:10.1007/s00332-023-09926-w.
short: K. Fellner, J.L. Fischer, M. Kniely, B.Q. Tang, Journal of Nonlinear Science
33 (2023).
date_created: 2021-12-16T12:15:35Z
date_published: 2023-06-07T00:00:00Z
date_updated: 2023-08-01T14:40:33Z
day: '07'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00332-023-09926-w
external_id:
arxiv:
- '2109.12019'
isi:
- '001002343400002'
file:
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creator: dernst
date_created: 2023-06-19T07:33:53Z
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language:
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month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global renormalised solutions and equilibration of reaction-diffusion systems
with non-linear diffusion
tmp:
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 33
year: '2023'
...
---
_id: '10551'
abstract:
- lang: eng
text: 'The Dean–Kawasaki equation—a strongly singular SPDE—is a basic equation of
fluctuating hydrodynamics; it has been proposed in the physics literature to describe
the fluctuations of the density of N independent diffusing particles in the regime
of large particle numbers N≫1. The singular nature of the Dean–Kawasaki equation
presents a substantial challenge for both its analysis and its rigorous mathematical
justification. Besides being non-renormalisable by the theory of regularity structures
by Hairer et al., it has recently been shown to not even admit nontrivial martingale
solutions. In the present work, we give a rigorous and fully quantitative justification
of the Dean–Kawasaki equation by considering the natural regularisation provided
by standard numerical discretisations: We show that structure-preserving discretisations
of the Dean–Kawasaki equation may approximate the density fluctuations of N non-interacting
diffusing particles to arbitrary order in N−1 (in suitable weak metrics). In
other words, the Dean–Kawasaki equation may be interpreted as a “recipe” for accurate
and efficient numerical simulations of the density fluctuations of independent
diffusing particles.'
acknowledgement: "We thank the anonymous referee for his/her careful reading of the
manuscript and valuable suggestions. FC gratefully acknowledges funding from the
Austrian Science Fund (FWF) through the project F65, and from the European Union’s
Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie
Grant Agreement No. 754411.\r\nOpen access funding provided by Austrian Science
Fund (FWF)."
article_number: '76'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Cornalba F, Fischer JL. The Dean-Kawasaki equation and the structure of density
fluctuations in systems of diffusing particles. Archive for Rational Mechanics
and Analysis. 2023;247(5). doi:10.1007/s00205-023-01903-7
apa: Cornalba, F., & Fischer, J. L. (2023). The Dean-Kawasaki equation and the
structure of density fluctuations in systems of diffusing particles. Archive
for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-023-01903-7
chicago: Cornalba, Federico, and Julian L Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2023. https://doi.org/10.1007/s00205-023-01903-7.
ieee: F. Cornalba and J. L. Fischer, “The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles,” Archive for Rational
Mechanics and Analysis, vol. 247, no. 5. Springer Nature, 2023.
ista: Cornalba F, Fischer JL. 2023. The Dean-Kawasaki equation and the structure
of density fluctuations in systems of diffusing particles. Archive for Rational
Mechanics and Analysis. 247(5), 76.
mla: Cornalba, Federico, and Julian L. Fischer. “The Dean-Kawasaki Equation and
the Structure of Density Fluctuations in Systems of Diffusing Particles.” Archive
for Rational Mechanics and Analysis, vol. 247, no. 5, 76, Springer Nature,
2023, doi:10.1007/s00205-023-01903-7.
short: F. Cornalba, J.L. Fischer, Archive for Rational Mechanics and Analysis 247
(2023).
corr_author: '1'
date_created: 2021-12-16T12:16:03Z
date_published: 2023-08-04T00:00:00Z
date_updated: 2025-04-23T13:06:01Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00205-023-01903-7
ec_funded: 1
external_id:
arxiv:
- '2109.06500'
isi:
- '001043086800001'
pmid:
- '37547904'
file:
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language:
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month: '08'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Dean-Kawasaki equation and the structure of density fluctuations in systems
of diffusing particles
tmp:
image: /images/cc_by.png
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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year: '2023'
...
---
OA_place: publisher
_id: '14587'
abstract:
- lang: eng
text: "This thesis concerns the application of variational methods to the study
of evolution problems arising in fluid mechanics and in material sciences. The
main focus is on weak-strong stability properties of some curvature driven interface
evolution problems, such as the two-phase Navier–Stokes flow with surface tension
and multiphase mean curvature flow, and on the phase-field approximation of the
latter. Furthermore, we discuss a variational approach to the study of a class
of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes
flow with surface tension within a bounded domain. The two fluids are immiscible
and separated by a sharp interface, which intersects the boundary of the domain
at a constant contact angle of ninety degree. We devise a suitable concept of
varifolds solutions for the associated interface evolution problem and we establish
a weak-strong uniqueness principle in case of a two dimensional ambient space.
In order to focus on the boundary effects and on the singular geometry of the
evolving domains, we work for simplicity in the regime of same viscosities for
the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the
convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature
flow for a suitable class of multi- well potentials and for well-prepared initial
data. We even establish a rate of convergence. Our relative energy approach relies
on the concept of gradient-flow calibration for branching singularities in multiphase
mean curvature flow and thus enables us to overcome the limitations of other approaches.
To the best of the author’s knowledge, our result is the first quantitative and
unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis
thesis also contains a first study of weak-strong stability for planar multiphase
mean curvature flow beyond the singularity resulting from a topology change. Previous
weak-strong results are indeed limited to time horizons before the first topology
change of the strong solution. We consider circular topology changes and we prove
weak-strong stability for BV solutions to planar multiphase mean curvature flow
beyond the associated singular times by dynamically adapting the strong solutions
to the weak one by means of a space-time shift.\r\nIn the context of interface
evolution problems, our proofs for the main results of this thesis are based on
the relative energy technique, relying on novel suitable notions of relative energy
functionals, which in particular measure the interface error. Our statements follow
from the resulting stability estimates for the relative energy associated to the
problem.\r\nAt last, we introduce a variational approach to the study of nonlinear
evolution problems. This approach hinges on the minimization of a parameter dependent
family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy
(WIDE) functionals. We consider a class of doubly nonlinear wave equations and
establish the convergence, up to subsequences, of the associated WIDE minimizers
to a solution of the target problem as the parameter goes to zero."
acknowledgement: The research projects contained in this thesis have received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 948819).
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Marveggio A. Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587
apa: Marveggio, A. (2023). Weak-strong stability and phase-field approximation
of interface evolution problems in fluid mechanics and in material sciences.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587
chicago: Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation
of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587.
ieee: A. Marveggio, “Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences,” Institute of
Science and Technology Austria, 2023.
ista: Marveggio A. 2023. Weak-strong stability and phase-field approximation of
interface evolution problems in fluid mechanics and in material sciences. Institute
of Science and Technology Austria.
mla: Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of
Interface Evolution Problems in Fluid Mechanics and in Material Sciences.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.
short: A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface
Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science
and Technology Austria, 2023.
corr_author: '1'
date_created: 2023-11-21T11:41:05Z
date_published: 2023-11-21T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '21'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:14587
ec_funded: 1
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month: '11'
oa: 1
oa_version: Published Version
page: '228'
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '11842'
relation: part_of_dissertation
status: public
- id: '14597'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: Weak-strong stability and phase-field approximation of interface evolution
problems in fluid mechanics and in material sciences
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user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...
---
_id: '11701'
abstract:
- lang: eng
text: In this paper we develop a new approach to nonlinear stochastic partial differential
equations with Gaussian noise. Our aim is to provide an abstract framework which
is applicable to a large class of SPDEs and includes many important cases of nonlinear
parabolic problems which are of quasi- or semilinear type. This first part is
on local existence and well-posedness. A second part in preparation is on blow-up
criteria and regularization. Our theory is formulated in an Lp-setting, and because
of this we can deal with nonlinearities in a very efficient way. Applications
to several concrete problems and their quasilinear variants are given. This includes
Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion
equations, and the porous media equation. The interplay of the nonlinearities
and the critical spaces of initial data leads to new results and insights for
these SPDEs. The proofs are based on recent developments in maximal regularity
theory for the linearized problem for deterministic and stochastic evolution equations.
In particular, our theory can be seen as a stochastic version of the theory of
critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity
allow us to deal with rough initial values and obtain instantaneous regularization
results. The abstract well-posedness results are obtained by a combination of
several sophisticated splitting and truncation arguments.
acknowledgement: The second author is supported by the VIDI subsidy 639.032.427 of
the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in
critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity.
2022;35(8):4100-4210. doi:10.1088/1361-6544/abd613
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/abd613
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity. IOP Publishing, 2022. https://doi.org/10.1088/1361-6544/abd613.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence,”
Nonlinearity, vol. 35, no. 8. IOP Publishing, pp. 4100–4210, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. 35(8), 4100–4210.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity, vol. 35, no. 8, IOP Publishing, 2022, pp. 4100–210, doi:10.1088/1361-6544/abd613.
short: A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210.
date_created: 2022-07-31T22:01:47Z
date_published: 2022-08-04T00:00:00Z
date_updated: 2023-08-03T12:25:08Z
day: '04'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1088/1361-6544/abd613
external_id:
arxiv:
- '2001.00512'
isi:
- '000826695900001'
file:
- access_level: open_access
checksum: 997a4bff2dfbee3321d081328c2f1e1a
content_type: application/pdf
creator: dernst
date_created: 2022-08-01T10:39:36Z
date_updated: 2022-08-01T10:39:36Z
file_id: '11715'
file_name: 2022_Nonlinearity_Agresti.pdf
file_size: 2122096
relation: main_file
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file_date_updated: 2022-08-01T10:39:36Z
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language:
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month: '08'
oa: 1
oa_version: Published Version
page: 4100-4210
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
issn:
- 0951-7715
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces Part
I. Stochastic maximal regularity and local existence
tmp:
image: /images/cc_by.png
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name: Creative Commons Attribution 3.0 Unported (CC BY 3.0)
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user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 35
year: '2022'
...
---
_id: '11858'
abstract:
- lang: eng
text: "This paper is a continuation of Part I of this project, where we developed
a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian
noise. In the current Part II we consider blow-up criteria and regularization
phenomena. As in Part I we can allow nonlinearities with polynomial growth and
rough initial values from critical spaces. In the first main result we obtain
several new blow-up criteria for quasi- and semilinear stochastic evolution equations.
In particular, for semilinear equations we obtain a Serrin type blow-up criterium,
which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074,
2018) to the stochastic setting. Blow-up criteria can be used to prove global
well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights
in time play a central role in the proofs. Our second contribution is a new method
to bootstrap Sobolev and Hölder regularity in time and space, which does not require
smoothness of the initial data. The blow-up criteria are at the basis of these
new methods. Moreover, in applications the bootstrap results can be combined with
our blow-up criteria, to obtain efficient ways to prove global existence. This
gives new results even in classical \U0001D43F2-settings, which we illustrate
for a concrete SPDE. In future works in preparation we apply the results of the
current paper to obtain global well-posedness results and regularity for several
concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion
equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into
a more flexible framework, where less restrictions on the nonlinearities are needed,
and we are able to treat rough initial values from critical spaces. Moreover,
we will obtain higher-order regularity results."
acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors
thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '56'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Nonlinear parabolic stochastic evolution equations in
critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces part II. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00786-7
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations.
Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces part II,” Journal of Evolution Equations, vol. 22, no.
2. Springer Nature, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces part II. Journal of Evolution Equations. 22(2), 56.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations,
vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7.
short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).
corr_author: '1'
date_created: 2022-08-16T08:39:43Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2024-10-09T21:03:06Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00028-022-00786-7
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- '000809108500001'
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keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces part
II
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
year: '2022'
...
---
_id: '12079'
abstract:
- lang: eng
text: We extend the recent rigorous convergence result of Abels and Moser (SIAM
J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning
convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin
boundary condition towards evolution by mean curvature flow with constant contact
angle. More precisely, in the present work we manage to remove the perturbative
assumption on the contact angle being close to 90∘. We establish under usual double-well
type assumptions on the potential and for a certain class of boundary energy densities
the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π).
For a very specific form of the boundary energy density, we even obtain from our
methods a sharp convergence rate of order ε; again for general contact angles
α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic
expansions and stability estimates for the linearized Allen–Cahn operator. Instead,
we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233,
2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy
technique. We develop a careful adaptation of their approach in order to encode
the constant contact angle condition. In fact, we perform this task at the level
of the notion of gradient flow calibrations. This concept was recently introduced
in the context of weak-strong uniqueness for multiphase mean curvature flow by
Fischer et al. (arXiv:2003.05478v2).
acknowledgement: "This Project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No 948819) , and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy—EXC-2047/1 - 390685813.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_number: '201'
article_processing_charge: No
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: 'Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary
contact energy: The non-perturbative regime. Calculus of Variations and Partial
Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3'
apa: 'Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation
with boundary contact energy: The non-perturbative regime. Calculus of Variations
and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3'
chicago: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.'
ieee: 'S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime,” Calculus of Variations
and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.'
ista: 'Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime. Calculus of Variations and
Partial Differential Equations. 61(6), 201.'
mla: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer
Nature, 2022, doi:10.1007/s00526-022-02307-3.'
short: S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations
61 (2022).
date_created: 2022-09-11T22:01:54Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2025-04-14T07:53:59Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00526-022-02307-3
ec_funded: 1
external_id:
isi:
- '000844247300008'
file:
- access_level: open_access
checksum: b2da020ce50440080feedabeab5b09c4
content_type: application/pdf
creator: dernst
date_created: 2023-01-20T08:56:01Z
date_updated: 2023-01-20T08:56:01Z
file_id: '12320'
file_name: 2022_Calculus_Hensel.pdf
file_size: 1278493
relation: main_file
success: 1
file_date_updated: 2023-01-20T08:56:01Z
has_accepted_license: '1'
intvolume: ' 61'
isi: 1
issue: '6'
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Convergence rates for the Allen–Cahn equation with boundary contact energy:
The non-perturbative regime'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 61
year: '2022'
...
---
_id: '12304'
abstract:
- lang: eng
text: 'We establish sharp criteria for the instantaneous propagation of free boundaries
in solutions to the thin-film equation. The criteria are formulated in terms of
the initial distribution of mass (as opposed to previous almost-optimal results),
reflecting the fact that mass is a locally conserved quantity for the thin-film
equation. In the regime of weak slippage, our criteria are at the same time necessary
and sufficient. The proof of our upper bounds on free boundary propagation is
based on a strategy of “propagation of degeneracy” down to arbitrarily small spatial
scales: We combine estimates on the local mass and estimates on energies to show
that “degeneracy” on a certain space-time cylinder entails “degeneracy” on a spatially
smaller space-time cylinder with the same time horizon. The derivation of our
lower bounds on free boundary propagation is based on a combination of a monotone
quantity and almost optimal estimates established previously by the second author
with a new estimate connecting motion of mass to entropy production.'
acknowledgement: N. De Nitti acknowledges the kind hospitality of IST Austria within
the framework of the ISTernship Summer Program 2018, during which most of the present
article was written. N. DeNitti has received funding by The Austrian Agency for
International Cooperation in Education &Research (OeAD-GmbH) via its financial support
of the ISTernship Summer Program 2018. N.De Nitti would also like to thank Giuseppe
Coclite, Giuseppe Devillanova, Giuseppe Florio, Sebastian Hensel, and Francesco
Maddalena for several helpful conversations on topics related to this work.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicola
full_name: De Nitti, Nicola
last_name: De Nitti
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: De Nitti N, Fischer JL. Sharp criteria for the waiting time phenomenon in solutions
to the thin-film equation. Communications in Partial Differential Equations.
2022;47(7):1394-1434. doi:10.1080/03605302.2022.2056702
apa: De Nitti, N., & Fischer, J. L. (2022). Sharp criteria for the waiting time
phenomenon in solutions to the thin-film equation. Communications in Partial
Differential Equations. Taylor & Francis. https://doi.org/10.1080/03605302.2022.2056702
chicago: De Nitti, Nicola, and Julian L Fischer. “Sharp Criteria for the Waiting
Time Phenomenon in Solutions to the Thin-Film Equation.” Communications in
Partial Differential Equations. Taylor & Francis, 2022. https://doi.org/10.1080/03605302.2022.2056702.
ieee: N. De Nitti and J. L. Fischer, “Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation,” Communications in Partial Differential
Equations, vol. 47, no. 7. Taylor & Francis, pp. 1394–1434, 2022.
ista: De Nitti N, Fischer JL. 2022. Sharp criteria for the waiting time phenomenon
in solutions to the thin-film equation. Communications in Partial Differential
Equations. 47(7), 1394–1434.
mla: De Nitti, Nicola, and Julian L. Fischer. “Sharp Criteria for the Waiting Time
Phenomenon in Solutions to the Thin-Film Equation.” Communications in Partial
Differential Equations, vol. 47, no. 7, Taylor & Francis, 2022, pp. 1394–434,
doi:10.1080/03605302.2022.2056702.
short: N. De Nitti, J.L. Fischer, Communications in Partial Differential Equations
47 (2022) 1394–1434.
corr_author: '1'
date_created: 2023-01-16T10:06:50Z
date_published: 2022-07-01T00:00:00Z
date_updated: 2024-10-09T21:03:57Z
day: '01'
department:
- _id: JuFi
doi: 10.1080/03605302.2022.2056702
external_id:
arxiv:
- '1907.05342'
isi:
- '000805689800001'
intvolume: ' 47'
isi: 1
issue: '7'
keyword:
- Applied Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.1907.05342'
month: '07'
oa: 1
oa_version: Preprint
page: 1394-1434
publication: Communications in Partial Differential Equations
publication_identifier:
eissn:
- 1532-4133
issn:
- 0360-5302
publication_status: published
publisher: Taylor & Francis
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sharp criteria for the waiting time phenomenon in solutions to the thin-film
equation
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 47
year: '2022'
...
---
_id: '12305'
abstract:
- lang: eng
text: This paper is concerned with the sharp interface limit for the Allen--Cahn
equation with a nonlinear Robin boundary condition in a bounded smooth domain
Ω⊂\R2. We assume that a diffuse interface already has developed and that it is
in contact with the boundary ∂Ω. The boundary condition is designed in such a
way that the limit problem is given by the mean curvature flow with constant α-contact
angle. For α close to 90° we prove a local in time convergence result for well-prepared
initial data for times when a smooth solution to the limit problem exists. Based
on the latter we construct a suitable curvilinear coordinate system and carry
out a rigorous asymptotic expansion for the Allen--Cahn equation with the nonlinear
Robin boundary condition. Moreover, we show a spectral estimate for the corresponding
linearized Allen--Cahn operator and with its aid we derive strong norm estimates
for the difference of the exact and approximate solutions using a Gronwall-type
argument.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Moser M. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 2022;54(1):114-172. doi:10.1137/21m1424925
apa: Abels, H., & Moser, M. (2022). Convergence of the Allen--Cahn equation
with a nonlinear Robin boundary condition to mean curvature flow with contact
angle close to 90°. SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics. https://doi.org/10.1137/21m1424925
chicago: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2022. https://doi.org/10.1137/21m1424925.
ieee: H. Abels and M. Moser, “Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°,”
SIAM Journal on Mathematical Analysis, vol. 54, no. 1. Society for Industrial
and Applied Mathematics, pp. 114–172, 2022.
ista: Abels H, Moser M. 2022. Convergence of the Allen--Cahn equation with a nonlinear
Robin boundary condition to mean curvature flow with contact angle close to 90°.
SIAM Journal on Mathematical Analysis. 54(1), 114–172.
mla: Abels, Helmut, and Maximilian Moser. “Convergence of the Allen--Cahn Equation
with a Nonlinear Robin Boundary Condition to Mean Curvature Flow with Contact
Angle Close to 90°.” SIAM Journal on Mathematical Analysis, vol. 54, no.
1, Society for Industrial and Applied Mathematics, 2022, pp. 114–72, doi:10.1137/21m1424925.
short: H. Abels, M. Moser, SIAM Journal on Mathematical Analysis 54 (2022) 114–172.
corr_author: '1'
date_created: 2023-01-16T10:07:00Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2024-10-09T21:03:58Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/21m1424925
external_id:
arxiv:
- '2105.08434'
isi:
- '000762768000004'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2105.08434'
month: '01'
oa: 1
oa_version: Preprint
page: 114-172
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Convergence of the Allen--Cahn equation with a nonlinear Robin boundary condition
to mean curvature flow with contact angle close to 90°
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10547'
abstract:
- lang: eng
text: "We establish global-in-time existence results for thermodynamically consistent
reaction-(cross-)diffusion systems coupled to an equation describing heat transfer.
Our main interest is to model species-dependent diffusivities,\r\nwhile at the
same time ensuring thermodynamic consistency. A key difficulty of the non-isothermal
case lies in the intrinsic presence of cross-diffusion type phenomena like the
Soret and the Dufour effect: due to the temperature/energy dependence of the thermodynamic
equilibria, a nonvanishing temperature gradient may drive a concentration flux
even in a situation with constant concentrations; likewise, a nonvanishing concentration
gradient may drive a heat flux even in a case of spatially constant temperature.
We use time discretisation and regularisation techniques and derive a priori estimates
based on a suitable entropy and the associated entropy production. Renormalised
solutions are used in cases where non-integrable diffusion fluxes or reaction
terms appear."
acknowledgement: M.K. gratefully acknowledges the hospitality of WIAS Berlin, where
a major part of the project was carried out. The research stay of M.K. at WIAS Berlin
was funded by the Austrian Federal Ministry of Education, Science and Research through
a research fellowship for graduates of a promotio sub auspiciis. The research of
A.M. has been partially supported by Deutsche Forschungsgemeinschaft (DFG) through
the Collaborative Research Center SFB 1114 “Scaling Cascades in Complex Systems”
(Project no. 235221301), Subproject C05 “Effective models for materials and interfaces
with multiple scales”. J.F. and A.M. are grateful for the hospitality of the Erwin
Schrödinger Institute in Vienna, where some ideas for this work have been developed.
The authors are grateful to two anonymous referees for several helpful comments,
in particular for the short proof of estimate (2.7).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Katharina
full_name: Hopf, Katharina
last_name: Hopf
- first_name: Michael
full_name: Kniely, Michael
id: 2CA2C08C-F248-11E8-B48F-1D18A9856A87
last_name: Kniely
orcid: 0000-0001-5645-4333
- first_name: Alexander
full_name: Mielke, Alexander
last_name: Mielke
citation:
ama: Fischer JL, Hopf K, Kniely M, Mielke A. Global existence analysis of energy-reaction-diffusion
systems. SIAM Journal on Mathematical Analysis. 2022;54(1):220-267. doi:10.1137/20M1387237
apa: Fischer, J. L., Hopf, K., Kniely, M., & Mielke, A. (2022). Global existence
analysis of energy-reaction-diffusion systems. SIAM Journal on Mathematical
Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/20M1387237
chicago: Fischer, Julian L, Katharina Hopf, Michael Kniely, and Alexander Mielke.
“Global Existence Analysis of Energy-Reaction-Diffusion Systems.” SIAM Journal
on Mathematical Analysis. Society for Industrial and Applied Mathematics,
2022. https://doi.org/10.1137/20M1387237.
ieee: J. L. Fischer, K. Hopf, M. Kniely, and A. Mielke, “Global existence analysis
of energy-reaction-diffusion systems,” SIAM Journal on Mathematical Analysis,
vol. 54, no. 1. Society for Industrial and Applied Mathematics, pp. 220–267, 2022.
ista: Fischer JL, Hopf K, Kniely M, Mielke A. 2022. Global existence analysis of
energy-reaction-diffusion systems. SIAM Journal on Mathematical Analysis. 54(1),
220–267.
mla: Fischer, Julian L., et al. “Global Existence Analysis of Energy-Reaction-Diffusion
Systems.” SIAM Journal on Mathematical Analysis, vol. 54, no. 1, Society
for Industrial and Applied Mathematics, 2022, pp. 220–67, doi:10.1137/20M1387237.
short: J.L. Fischer, K. Hopf, M. Kniely, A. Mielke, SIAM Journal on Mathematical
Analysis 54 (2022) 220–267.
date_created: 2021-12-16T12:08:56Z
date_published: 2022-01-04T00:00:00Z
date_updated: 2023-08-02T13:37:03Z
day: '04'
department:
- _id: JuFi
doi: 10.1137/20M1387237
external_id:
arxiv:
- '2012.03792 '
isi:
- '000762768000006'
intvolume: ' 54'
isi: 1
issue: '1'
keyword:
- Energy-Reaction-Diffusion Systems
- Cross Diffusion
- Global-In-Time Existence of Weak/Renormalised Solutions
- Entropy Method
- Onsager System
- Soret/Dufour Effect
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2012.03792
month: '01'
oa: 1
oa_version: Preprint
page: 220-267
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Global existence analysis of energy-reaction-diffusion systems
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 54
year: '2022'
...
---
_id: '10548'
abstract:
- lang: eng
text: "Consider a linear elliptic partial differential equation in divergence form
with a random coefficient field. The solution operator displays fluctuations around
its expectation. The recently developed pathwise theory of fluctuations in stochastic
homogenization reduces the characterization of these fluctuations to those of
the so-called standard homogenization commutator. In this contribution, we investigate
the scaling limit of this key quantity: starting\r\nfrom a Gaussian-like coefficient
field with possibly strong correlations, we establish the convergence of the rescaled
commutator to a fractional Gaussian field, depending on the decay of correlations
of the coefficient field, and we\r\ninvestigate the (non)degeneracy of the limit.
This extends to general dimension $d\\ge1$ previous results so far limited to
dimension $d=1$, and to the continuum setting with strong correlations recent
results in the discrete iid case."
acknowledgement: The authors thank Ivan Nourdin and Felix Otto for inspiring discussions.
The work of MD is financially supported by the CNRS-Momentum program. Financial
support of AG is acknowledged from the European Research Council under the European
Community’s Seventh Framework Programme (FP7/2014-2019 Grant Agreement QUANTHOM
335410).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mitia
full_name: Duerinckx, Mitia
last_name: Duerinckx
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Antoine
full_name: Gloria, Antoine
last_name: Gloria
citation:
ama: Duerinckx M, Fischer JL, Gloria A. Scaling limit of the homogenization commutator
for Gaussian coefficient fields. Annals of applied probability. 2022;32(2):1179-1209.
doi:10.1214/21-AAP1705
apa: Duerinckx, M., Fischer, J. L., & Gloria, A. (2022). Scaling limit of the
homogenization commutator for Gaussian coefficient fields. Annals of Applied
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AAP1705
chicago: Duerinckx, Mitia, Julian L Fischer, and Antoine Gloria. “Scaling Limit
of the Homogenization Commutator for Gaussian Coefficient Fields.” Annals
of Applied Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AAP1705.
ieee: M. Duerinckx, J. L. Fischer, and A. Gloria, “Scaling limit of the homogenization
commutator for Gaussian coefficient fields,” Annals of applied probability,
vol. 32, no. 2. Institute of Mathematical Statistics, pp. 1179–1209, 2022.
ista: Duerinckx M, Fischer JL, Gloria A. 2022. Scaling limit of the homogenization
commutator for Gaussian coefficient fields. Annals of applied probability. 32(2),
1179–1209.
mla: Duerinckx, Mitia, et al. “Scaling Limit of the Homogenization Commutator for
Gaussian Coefficient Fields.” Annals of Applied Probability, vol. 32,
no. 2, Institute of Mathematical Statistics, 2022, pp. 1179–209, doi:10.1214/21-AAP1705.
short: M. Duerinckx, J.L. Fischer, A. Gloria, Annals of Applied Probability 32 (2022)
1179–1209.
corr_author: '1'
date_created: 2021-12-16T12:10:16Z
date_published: 2022-04-28T00:00:00Z
date_updated: 2024-10-09T21:01:17Z
day: '28'
department:
- _id: JuFi
doi: 10.1214/21-AAP1705
external_id:
arxiv:
- '1910.04088'
isi:
- '000791003700011'
intvolume: ' 32'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1910.04088
month: '04'
oa: 1
oa_version: Preprint
page: 1179-1209
publication: Annals of applied probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scaling limit of the homogenization commutator for Gaussian coefficient fields
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 32
year: '2022'
...