Invariant manifolds for stochastic delayed partial differential equations of parabolic type

The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is firstly transformed into a random delayed partial differential e...

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Detalles Bibliográficos
Autores: Hu, Wenjie, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2023
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/150170
Acceso en línea:https://hdl.handle.net/11441/150170
https://doi.org/10.1016/j.chaos.2023.114189
Access Level:acceso abierto
Palabra clave:Invariant manifolds
stochastic partial differential equations
delay
random dynamical systems
Lyapunov-Perron’s method
smoothness
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spelling Invariant manifolds for stochastic delayed partial differential equations of parabolic typeHu, WenjieCaraballo Garrido, TomásInvariant manifoldsstochastic partial differential equationsdelayrandom dynamical systemsLyapunov-Perron’s methodsmoothnessThe aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is firstly transformed into a random delayed partial differential equation by a conjugation, which is then recast into a Hilbert space. For the auxiliary equation, the variation of constants formula holds and we show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron method. Subsequently, we prove the smoothness of these invariant manifolds under appropriate spectral gap condition by carefully investigating the smoothness of auxiliary equation, after which, we obtain the invariant manifolds of the original equation by projection and inverse transformation. Eventually, we illustrate the obtained theoretical results by their application to a stochastic single-species population model.ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/150170https://doi.org/10.1016/j.chaos.2023.114189reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésChaos, Solitons & Fractals, 176 (noviembre), 114189-1.https://doi.org/10.1016/j.chaos.2023.114189info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1501702026-06-17T12:51:07Z
dc.title.none.fl_str_mv Invariant manifolds for stochastic delayed partial differential equations of parabolic type
title Invariant manifolds for stochastic delayed partial differential equations of parabolic type
spellingShingle Invariant manifolds for stochastic delayed partial differential equations of parabolic type
Hu, Wenjie
Invariant manifolds
stochastic partial differential equations
delay
random dynamical systems
Lyapunov-Perron’s method
smoothness
title_short Invariant manifolds for stochastic delayed partial differential equations of parabolic type
title_full Invariant manifolds for stochastic delayed partial differential equations of parabolic type
title_fullStr Invariant manifolds for stochastic delayed partial differential equations of parabolic type
title_full_unstemmed Invariant manifolds for stochastic delayed partial differential equations of parabolic type
title_sort Invariant manifolds for stochastic delayed partial differential equations of parabolic type
dc.creator.none.fl_str_mv Hu, Wenjie
Caraballo Garrido, Tomás
author Hu, Wenjie
author_facet Hu, Wenjie
Caraballo Garrido, Tomás
author_role author
author2 Caraballo Garrido, Tomás
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Invariant manifolds
stochastic partial differential equations
delay
random dynamical systems
Lyapunov-Perron’s method
smoothness
topic Invariant manifolds
stochastic partial differential equations
delay
random dynamical systems
Lyapunov-Perron’s method
smoothness
description The aim of this paper is to prove the existence and smoothness of stable and unstable invariant manifolds for a stochastic delayed partial differential equation of parabolic type. The stochastic delayed partial differential equation is firstly transformed into a random delayed partial differential equation by a conjugation, which is then recast into a Hilbert space. For the auxiliary equation, the variation of constants formula holds and we show the existence of Lipschitz continuous stable and unstable manifolds by the Lyapunov-Perron method. Subsequently, we prove the smoothness of these invariant manifolds under appropriate spectral gap condition by carefully investigating the smoothness of auxiliary equation, after which, we obtain the invariant manifolds of the original equation by projection and inverse transformation. Eventually, we illustrate the obtained theoretical results by their application to a stochastic single-species population model.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/150170
https://doi.org/10.1016/j.chaos.2023.114189
url https://hdl.handle.net/11441/150170
https://doi.org/10.1016/j.chaos.2023.114189
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Chaos, Solitons & Fractals, 176 (noviembre), 114189-1.
https://doi.org/10.1016/j.chaos.2023.114189
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300724

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