Continuity and topological structural stability for nonautonomous random attractors

In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study the existence and permanence of unstable sets of hyperbolic solut...

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Autores: Caraballo Garrido, Tomás, Carvalho, Alexandre N., Langa Rosado, José Antonio, Oliveira Sousa, Alexandre N.
Tipo de documento: artigo
Estado:Versión enviada para evaluación y publicación
Data de publicação:2021
País:España
Recursos:Universidad de Sevilla (US)
Repositório:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/147927
Acesso em linha:https://hdl.handle.net/11441/147927
https://doi.org/10.1142/S021949372240024X
Access Level:Acceso aberto
Palavra-chave:Nonautonomous random dynamical systems
continuity of attractors
topological structural stability
bounded noise
damped wave equation
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spelling Continuity and topological structural stability for nonautonomous random attractorsCaraballo Garrido, TomásCarvalho, Alexandre N.Langa Rosado, José AntonioOliveira Sousa, Alexandre N.Nonautonomous random dynamical systemscontinuity of attractorstopological structural stabilitybounded noisedamped wave equationIn this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study the existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to establish the lower semicontinuity of nonautonomous random attractors and to show that the gradient structure persists under nonautonomous random perturbations. Finally, we apply the abstract results in a stochastic differential equation and in a damped wave equation with a perturbation on the damping.World scientificEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/147927https://doi.org/10.1142/S021949372240024Xreponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésStochastics and Dynamics, 22 (7), 2240024-1.https://doi.org/10.1142/S021949372240024Xinfo:eu-repo/semantics/openAccessoai:idus.us.es:11441/1479272026-06-17T12:51:07Z
dc.title.none.fl_str_mv Continuity and topological structural stability for nonautonomous random attractors
title Continuity and topological structural stability for nonautonomous random attractors
spellingShingle Continuity and topological structural stability for nonautonomous random attractors
Caraballo Garrido, Tomás
Nonautonomous random dynamical systems
continuity of attractors
topological structural stability
bounded noise
damped wave equation
title_short Continuity and topological structural stability for nonautonomous random attractors
title_full Continuity and topological structural stability for nonautonomous random attractors
title_fullStr Continuity and topological structural stability for nonautonomous random attractors
title_full_unstemmed Continuity and topological structural stability for nonautonomous random attractors
title_sort Continuity and topological structural stability for nonautonomous random attractors
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Carvalho, Alexandre N.
Langa Rosado, José Antonio
Oliveira Sousa, Alexandre N.
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Carvalho, Alexandre N.
Langa Rosado, José Antonio
Oliveira Sousa, Alexandre N.
author_role author
author2 Carvalho, Alexandre N.
Langa Rosado, José Antonio
Oliveira Sousa, Alexandre N.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Nonautonomous random dynamical systems
continuity of attractors
topological structural stability
bounded noise
damped wave equation
topic Nonautonomous random dynamical systems
continuity of attractors
topological structural stability
bounded noise
damped wave equation
description In this work, we study the continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study the existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to establish the lower semicontinuity of nonautonomous random attractors and to show that the gradient structure persists under nonautonomous random perturbations. Finally, we apply the abstract results in a stochastic differential equation and in a damped wave equation with a perturbation on the damping.
publishDate 2021
dc.date.none.fl_str_mv 2021
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/11441/147927
https://doi.org/10.1142/S021949372240024X
url https://hdl.handle.net/11441/147927
https://doi.org/10.1142/S021949372240024X
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Stochastics and Dynamics, 22 (7), 2240024-1.
https://doi.org/10.1142/S021949372240024X
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 World scientific
publisher.none.fl_str_mv World scientific
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 15.228081

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