---
_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. <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>. 2023;11:1254–1378. doi:<a href="https://doi.org/10.1007/s40072-022-00254-w">10.1007/s40072-022-00254-w</a>'
  apa: 'Clozeau, N. (2023). Optimal decay of the parabolic semigroup in stochastic
    homogenization  for correlated coefficient fields. <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>. Springer Nature. <a href="https://doi.org/10.1007/s40072-022-00254-w">https://doi.org/10.1007/s40072-022-00254-w</a>'
  chicago: 'Clozeau, Nicolas. “Optimal Decay of the Parabolic Semigroup in Stochastic
    Homogenization  for Correlated Coefficient Fields.” <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>. Springer Nature, 2023.
    <a href="https://doi.org/10.1007/s40072-022-00254-w">https://doi.org/10.1007/s40072-022-00254-w</a>.'
  ieee: 'N. Clozeau, “Optimal decay of the parabolic semigroup in stochastic homogenization 
    for correlated coefficient fields,” <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>, 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.” <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>, vol. 11, Springer Nature,
    2023, pp. 1254–1378, doi:<a href="https://doi.org/10.1007/s40072-022-00254-w">10.1007/s40072-022-00254-w</a>.'
  short: 'N. Clozeau, Stochastics and Partial Differential Equations: Analysis and
    Computations 11 (2023) 1254–1378.'
date_created: 2021-10-23T10:50:22Z
date_published: 2023-09-01T00:00:00Z
date_updated: 2023-08-14T11:51:47Z
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: '12486'
abstract:
- lang: eng
  text: This paper is concerned with the problem of regularization by noise of systems
    of reaction–diffusion equations with mass control. It is known that strong solutions
    to such systems of PDEs may blow-up in finite time. Moreover, for many systems
    of practical interest, establishing whether the blow-up occurs or not is an open
    question. Here we prove that a suitable multiplicative noise of transport type
    has a regularizing effect. More precisely, for both a sufficiently noise intensity
    and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary
    large time. Global existence is shown for the case of exponentially decreasing
    mass. The proofs combine and extend recent developments in regularization by noise
    and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between
    the two areas.
acknowledgement: "The 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).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio
  Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti
  for her support in creating the picture. The author\r\nthanks the anonymous referee
  for helpful comments. "
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
citation:
  ama: 'Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems
    of reaction-diffusion equations. <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>. 2023. doi:<a href="https://doi.org/10.1007/s40072-023-00319-4">10.1007/s40072-023-00319-4</a>'
  apa: 'Agresti, A. (2023). Delayed blow-up and enhanced diffusion by transport noise
    for systems of reaction-diffusion equations. <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>. Springer Nature. <a href="https://doi.org/10.1007/s40072-023-00319-4">https://doi.org/10.1007/s40072-023-00319-4</a>'
  chicago: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport
    Noise for Systems of Reaction-Diffusion Equations.” <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>. Springer Nature, 2023.
    <a href="https://doi.org/10.1007/s40072-023-00319-4">https://doi.org/10.1007/s40072-023-00319-4</a>.'
  ieee: 'A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for
    systems of reaction-diffusion equations,” <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>. Springer Nature, 2023.'
  ista: 'Agresti A. 2023. Delayed blow-up and enhanced diffusion by transport noise
    for systems of reaction-diffusion equations. Stochastics and Partial Differential
    Equations: Analysis and Computations.'
  mla: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise
    for Systems of Reaction-Diffusion Equations.” <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>, Springer Nature, 2023, doi:<a href="https://doi.org/10.1007/s40072-023-00319-4">10.1007/s40072-023-00319-4</a>.'
  short: 'A. Agresti, Stochastics and Partial Differential Equations: Analysis and
    Computations (2023).'
date_created: 2023-02-02T10:45:47Z
date_published: 2023-11-28T00:00:00Z
date_updated: 2023-12-18T07:53:45Z
day: '28'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-023-00319-4
ec_funded: 1
external_id:
  arxiv:
  - '2207.08293'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s40072-023-00319-4
month: '11'
oa: 1
oa_version: Submitted Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
  call_identifier: H2020
  grant_number: '948819'
  name: Bridging Scales in Random Materials
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
  eissn:
  - 2194-041X
  issn:
  - 2194-0401
publication_status: epub_ahead
publisher: Springer Nature
scopus_import: '1'
status: public
title: Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion
  equations
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
year: '2023'
...
---
_id: '12178'
abstract:
- lang: eng
  text: In this paper we consider the stochastic primitive equation for geophysical
    flows subject to transport noise and turbulent pressure. Admitting very rough
    noise terms, the global existence and uniqueness of solutions to this stochastic
    partial differential equation are proven using stochastic maximal L² regularity,
    the theory of critical spaces for stochastic evolution equations, and global a
    priori bounds. Compared to other results in this direction, we do not need any
    smallness assumption on the transport noise which acts directly on the velocity
    field and we also allow rougher noise terms. The adaptation to Stratonovich type
    noise and, more generally, to variable viscosity and/or conductivity are discussed
    as well.
acknowledgement: The authors thank the anonymous referees for their helpful comments
  and suggestions. Open Access funding enabled and organized by Projekt DEAL.
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: Matthias
  full_name: Hieber, Matthias
  last_name: Hieber
- first_name: Amru
  full_name: Hussein, Amru
  last_name: Hussein
- first_name: Martin
  full_name: Saal, Martin
  last_name: Saal
citation:
  ama: 'Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations
    with transport noise and turbulent pressure. <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>. 2022. doi:<a href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a>'
  apa: 'Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2022). The stochastic
    primitive equations with transport noise and turbulent pressure. <i>Stochastics
    and Partial Differential Equations: Analysis and Computations</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a>'
  chicago: 'Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The
    Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics
    and Partial Differential Equations: Analysis and Computations</i>. Springer Nature,
    2022. <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a>.'
  ieee: 'A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive
    equations with transport noise and turbulent pressure,” <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>. Springer Nature, 2022.'
  ista: 'Agresti A, Hieber M, Hussein A, Saal M. 2022. The stochastic primitive equations
    with transport noise and turbulent pressure. Stochastics and Partial Differential
    Equations: Analysis and Computations.'
  mla: 'Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport
    Noise and Turbulent Pressure.” <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>, Springer Nature, 2022, doi:<a href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a>.'
  short: 'A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential
    Equations: Analysis and Computations (2022).'
date_created: 2023-01-12T12:12:29Z
date_published: 2022-10-27T00:00:00Z
date_updated: 2023-08-16T09:11:38Z
day: '27'
department:
- _id: JuFi
doi: 10.1007/s40072-022-00277-3
external_id:
  isi:
  - '000874389000001'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s40072-022-00277-3
month: '10'
oa: 1
oa_version: Published Version
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
  eissn:
  - 2194-041X
  issn:
  - 2194-0401
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: The stochastic primitive equations with transport noise and turbulent pressure
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
_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. <i>Stochastics and Partial Differential Equations: Analysis
    and Computations</i>. 2021;9:892–939. doi:<a href="https://doi.org/10.1007/s40072-021-00188-9">10.1007/s40072-021-00188-9</a>'
  apa: 'Hensel, S. (2021). Finite time extinction for the 1D stochastic porous medium
    equation with transport noise. <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>. Springer Nature. <a href="https://doi.org/10.1007/s40072-021-00188-9">https://doi.org/10.1007/s40072-021-00188-9</a>'
  chicago: 'Hensel, Sebastian. “Finite Time Extinction for the 1D Stochastic Porous
    Medium Equation with Transport Noise.” <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>. Springer Nature, 2021. <a href="https://doi.org/10.1007/s40072-021-00188-9">https://doi.org/10.1007/s40072-021-00188-9</a>.'
  ieee: 'S. Hensel, “Finite time extinction for the 1D stochastic porous medium equation
    with transport noise,” <i>Stochastics and Partial Differential Equations: Analysis
    and Computations</i>, 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.” <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>, vol. 9, Springer Nature, 2021, pp. 892–939, doi:<a
    href="https://doi.org/10.1007/s40072-021-00188-9">10.1007/s40072-021-00188-9</a>.'
  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'
...