---
_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
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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checksum: f3f0f0886098e31c81116cff8183750b
content_type: application/pdf
creator: dernst
date_created: 2023-06-19T07:33:53Z
date_updated: 2023-06-19T07:33:53Z
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file_name: 2023_JourNonlinearScience_Fellner.pdf
file_size: 742315
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file_date_updated: 2023-06-19T07:33:53Z
has_accepted_license: '1'
intvolume: ' 33'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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:
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: 33
year: '2023'
...