Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay

The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay. The stochastic equation is firstly transformed into a delayed random partial differential equation by means of a random conjugatio...

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Detalles Bibliográficos
Autores: Hu, Wenjie, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/164395
Acceso en línea:https://hdl.handle.net/11441/164395
https://doi.org/10.14232/ejqtde.2024.1.56
Access Level:acceso abierto
Palabra clave:Hausdorff dimension
Fractal dimension
Random dynamical system
Random attractors
Delay
Stochastic reaction-diffusion equations
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spelling Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delayHu, WenjieCaraballo Garrido, TomásHausdorff dimensionFractal dimensionRandom dynamical systemRandom attractorsDelayStochastic reaction-diffusion equationsThe aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay. The stochastic equation is firstly transformed into a delayed random partial differential equation by means of a random conjugation, which is then recast into an auxiliary Hilbert space. For the obtained equation, it is firstly proved that it generates a random dynamical system (RDS) in the auxiliary Hilbert space. Then it is shown that the equation possesses random attractors by a uniform estimate of the solution and the asymptotic compactness of the generated RDS. After establishing the variational equation in the auxiliary Hilbert space and the almost surely differentiable properties of the RDS, upper estimates of both Hausdorff and fractal dimensions of the random attractors are obtained.Bolyai Institute, University of SzegedEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2024info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/164395https://doi.org/10.14232/ejqtde.2024.1.56reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésElectronic Journal of Qualitative Theory of Differential Equations, 56, 1-23.https://doi.org/10.14232/ejqtde.2024.1.56info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1643952026-06-17T12:51:07Z
dc.title.none.fl_str_mv Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
title Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
spellingShingle Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
Hu, Wenjie
Hausdorff dimension
Fractal dimension
Random dynamical system
Random attractors
Delay
Stochastic reaction-diffusion equations
title_short Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
title_full Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
title_fullStr Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
title_full_unstemmed Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
title_sort Topological dimensions of random attractors for a stochastic reaction-diffusion equation with delay
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 Hausdorff dimension
Fractal dimension
Random dynamical system
Random attractors
Delay
Stochastic reaction-diffusion equations
topic Hausdorff dimension
Fractal dimension
Random dynamical system
Random attractors
Delay
Stochastic reaction-diffusion equations
description The aim of this paper is to obtain an estimation of Hausdorff as well as fractal dimensions of random attractors for a stochastic reaction-diffusion equation with delay. The stochastic equation is firstly transformed into a delayed random partial differential equation by means of a random conjugation, which is then recast into an auxiliary Hilbert space. For the obtained equation, it is firstly proved that it generates a random dynamical system (RDS) in the auxiliary Hilbert space. Then it is shown that the equation possesses random attractors by a uniform estimate of the solution and the asymptotic compactness of the generated RDS. After establishing the variational equation in the auxiliary Hilbert space and the almost surely differentiable properties of the RDS, upper estimates of both Hausdorff and fractal dimensions of the random attractors are obtained.
publishDate 2024
dc.date.none.fl_str_mv 2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/164395
https://doi.org/10.14232/ejqtde.2024.1.56
url https://hdl.handle.net/11441/164395
https://doi.org/10.14232/ejqtde.2024.1.56
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Electronic Journal of Qualitative Theory of Differential Equations, 56, 1-23.
https://doi.org/10.14232/ejqtde.2024.1.56
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 Bolyai Institute, University of Szeged
publisher.none.fl_str_mv Bolyai Institute, University of Szeged
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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