A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor

In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the non-linear term f. The function β"(t) depends on a parameter ε, β&q...

Descripción completa

Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Carvalho, Alexandre Nolasco, Langa Rosado, José Antonio, Rivero Garvía, Luis Felipe
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23632
Acceso en línea:http://hdl.handle.net/11441/23632
https://doi.org/10.1016/j.na.2010.11.032
Access Level:acceso abierto
Palabra clave:Non-autonomous damped wave equation
Existence and structure of the pullback attractor
Lower and upper semicontinuity
id ES_87d048ec2b8f4fbf5a71f32d9f2c9e3b
oai_identifier_str oai:idus.us.es:11441/23632
network_acronym_str ES
network_name_str España
repository_id_str
spelling A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback AttractorCaraballo Garrido, TomásCarvalho, Alexandre NolascoLanga Rosado, José AntonioRivero Garvía, Luis FelipeNon-autonomous damped wave equationExistence and structure of the pullback attractorLower and upper semicontinuityIn this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the non-linear term f. The function β"(t) depends on a parameter ε, β"(t) "!0 −→ 0. We will prove, under suitable assumptions, local and global well posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A"(t) : t ∈ R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at ǫ = 0.Ecuaciones Diferenciales y Análisis Numérico2011info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/23632https://doi.org/10.1016/j.na.2010.11.032reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Analysis, 74 2272-2283info:eu-repo/semantics/openAccessoai:idus.us.es:11441/236322026-06-17T12:51:07Z
dc.title.none.fl_str_mv A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
title A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
spellingShingle A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
Caraballo Garrido, Tomás
Non-autonomous damped wave equation
Existence and structure of the pullback attractor
Lower and upper semicontinuity
title_short A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
title_full A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
title_fullStr A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
title_full_unstemmed A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
title_sort A Non-Autonomous Strongly Damped Wave Equation: Existence and Continuity of the Pullback Attractor
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
author_role author
author2 Carvalho, Alexandre Nolasco
Langa Rosado, José Antonio
Rivero Garvía, Luis Felipe
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Non-autonomous damped wave equation
Existence and structure of the pullback attractor
Lower and upper semicontinuity
topic Non-autonomous damped wave equation
Existence and structure of the pullback attractor
Lower and upper semicontinuity
description In this paper we consider the strongly damped wave equation with time dependent terms utt − u − γ(t) ut + β"(t)ut = f(u), in a bounded domain ⊂ Rn, under some restrictions on β"(t), γ(t) and growth restrictions on the non-linear term f. The function β"(t) depends on a parameter ε, β"(t) "!0 −→ 0. We will prove, under suitable assumptions, local and global well posedness (using the uniform sectorial operators theory), the existence and regularity of pullback attractors {A"(t) : t ∈ R}, uniform bounds for these pullback attractors, characterization of these pullback attractors and their upper and lower semicontinuity at ǫ = 0.
publishDate 2011
dc.date.none.fl_str_mv 2011
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/23632
https://doi.org/10.1016/j.na.2010.11.032
url http://hdl.handle.net/11441/23632
https://doi.org/10.1016/j.na.2010.11.032
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Analysis, 74 2272-2283
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
_version_ 1869412489593094144
score 15,300719

Similares en LA Referencia