A gradient-like non autonomous evolution process

In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ­ ½ Rn with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping ¯ : R ! (0;1) is a suitable function. W...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Langa Rosado, José Antonio, Rivero Garvía, Luis Felipe, Carvalho, Alexandre Nolasco
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/24705
Acceso en línea:http://hdl.handle.net/11441/24705
Access Level:acceso abierto
Palabra clave:Pullback attractor
asymptotic compactness
evolution process
non-autonomous damped wave equation
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spelling A gradient-like non autonomous evolution processCaraballo Garrido, TomásLanga Rosado, José AntonioRivero Garvía, Luis FelipeCarvalho, Alexandre NolascoPullback attractorasymptotic compactnessevolution processnon-autonomous damped wave equationIn this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ­ ½ Rn with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping ¯ : R ! (0;1) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of non-autonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small non-autonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small non-autonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.Ecuaciones Diferenciales y Análisis Numérico2009info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/24705reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNotas. Série Matemática, 304, 1-15info:eu-repo/semantics/openAccessoai:idus.us.es:11441/247052026-06-17T12:51:07Z
dc.title.none.fl_str_mv A gradient-like non autonomous evolution process
title A gradient-like non autonomous evolution process
spellingShingle A gradient-like non autonomous evolution process
Caraballo Garrido, Tomás
Pullback attractor
asymptotic compactness
evolution process
non-autonomous damped wave equation
title_short A gradient-like non autonomous evolution process
title_full A gradient-like non autonomous evolution process
title_fullStr A gradient-like non autonomous evolution process
title_full_unstemmed A gradient-like non autonomous evolution process
title_sort A gradient-like non autonomous evolution process
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
Carvalho, Alexandre Nolasco
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
Carvalho, Alexandre Nolasco
author_role author
author2 Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
Carvalho, Alexandre Nolasco
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Pullback attractor
asymptotic compactness
evolution process
non-autonomous damped wave equation
topic Pullback attractor
asymptotic compactness
evolution process
non-autonomous damped wave equation
description In this paper we consider a dissipative damped wave equation with non-autonomous damping of the form utt + ¯(t)ut = ¢u + f(u) (1) in a bounded smooth domain ­ ½ Rn with Dirichlet boundary conditions, where f is a dissipative smooth nonlinearity and the damping ¯ : R ! (0;1) is a suitable function. We prove, if (1) has finitely many equilibria, that all global bounded solutions of (1) are backwards and forwards asymptotic to equilibria. Thus, we give a class of examples of non-autonomous evolution processes for which the structure of the pullback attractors is well understood. That complements the results of [Carvalho & Langa, 2009] on characterization of attractors, where it was shown that a small non-autonomous perturbation of an autonomous gradient-like evolution process is also gradient-like. Note that the evolution process associated to (1) is not a small non-autonomous perturbation of any autonomous gradient-like evolution processes. Moreover, we are also able to prove that the pullback attractor for (1) is also a forwards attractor and that the rate of attraction is exponential.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/24705
url http://hdl.handle.net/11441/24705
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Notas. Série Matemática, 304, 1-15
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.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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