---
_id: '9307'
abstract:
- lang: eng
text: We establish finite time extinction with probability one for weak solutions
of the Cauchy–Dirichlet problem for the 1D stochastic porous medium equation with
Stratonovich transport noise and compactly supported smooth initial datum. Heuristically,
this is expected to hold because Brownian motion has average spread rate O(t12)
whereas the support of solutions to the deterministic PME grows only with rate
O(t1m+1). The rigorous proof relies on a contraction principle up to time-dependent
shift for Wong–Zakai type approximations, the transformation to a deterministic
PME with two copies of a Brownian path as the lateral boundary, and techniques
from the theory of viscosity solutions.
acknowledgement: This project has received funding from the European Union’s Horizon
2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement
No. 665385 . I am very grateful to M. Gerencsér and J. Maas for proposing this problem
as well as helpful discussions. Special thanks go to F. Cornalba for suggesting
the additional κ-truncation in Proposition 5. I am also indebted to an anonymous
referee for pointing out a gap in a previous version of the proof of Lemma 9 (concerning
the treatment of the noise term). The issue is resolved in this version.
article_processing_charge: Yes (via OA deal)
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
citation:
ama: 'Hensel S. Finite time extinction for the 1D stochastic porous medium equation
with transport noise. Stochastics and Partial Differential Equations: Analysis
and Computations. 2021;9:892–939. doi:10.1007/s40072-021-00188-9'
apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-021-00188-9'
chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous
Medium Equation with Transport Noise.” Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature, 2021. https://doi.org/10.1007/s40072-021-00188-9.'
ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation
with transport noise,” Stochastics and Partial Differential Equations: Analysis
and Computations, vol. 9. Springer Nature, pp. 892–939, 2021.'
ista: 'Hensel S. 2021. Finite time extinction for the 1D stochastic porous medium
equation with transport noise. Stochastics and Partial Differential Equations:
Analysis and Computations. 9, 892–939.'
mla: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous Medium
Equation with Transport Noise.” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 9, Springer Nature, 2021, pp. 892–939, doi:10.1007/s40072-021-00188-9.'
short: 'S. Hensel, Stochastics and Partial Differential Equations: Analysis and
Computations 9 (2021) 892–939.'
date_created: 2021-04-04T22:01:21Z
date_published: 2021-03-21T00:00:00Z
date_updated: 2023-08-07T14:31:59Z
day: '21'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-021-00188-9
ec_funded: 1
external_id:
isi:
- '000631001700001'
file:
- access_level: open_access
checksum: 6529b609c9209861720ffa4685111bc6
content_type: application/pdf
creator: dernst
date_created: 2021-04-06T09:31:28Z
date_updated: 2021-04-06T09:31:28Z
file_id: '9309'
file_name: 2021_StochPartDiffEquation_Hensel.pdf
file_size: 727005
relation: main_file
success: 1
file_date_updated: 2021-04-06T09:31:28Z
has_accepted_license: '1'
intvolume: ' 9'
isi: 1
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 892–939
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finite time extinction for the 1D stochastic porous medium equation with transport
noise
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: 9
year: '2021'
...