Global attractor for a non-autonomous integro-differential equation in materials with memory

The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated in this paper. The assumptions imposed on the coefficients are weak in the...

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Autores: Caraballo Garrido, Tomás, Garrido Atienza, María José, Schmalfuss, Björn, Valero Cuadra, José
Tipo de recurso: artículo
Fecha de publicación:2010
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/23670
Acceso en línea:http://hdl.handle.net/11441/23670
https://doi.org/10.1016/j.na.2010.03.012
Access Level:acceso abierto
Palabra clave:Delayed reaction-diffusion equations
integro-differential equations with memory
non-autonomous (pullback) attractors
multivalued dynamical systems
asymptotic behavior
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spelling Global attractor for a non-autonomous integro-differential equation in materials with memoryCaraballo Garrido, TomásGarrido Atienza, María JoséSchmalfuss, BjörnValero Cuadra, JoséDelayed reaction-diffusion equationsintegro-differential equations with memorynon-autonomous (pullback) attractorsmultivalued dynamical systemsasymptotic behaviorThe long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated in this paper. The assumptions imposed on the coefficients are weak in the sense that uniqueness of solutions of the corresponding initial value problems cannot be guaranteed. Then, it is proved that the model generates a multivalued non–autonomous dynamical system which possesses a pullback attractor. First, the analysis is carried out with an abstract parabolic equation. Then, the theory is applied to the particular integro-differential equation which is the objective of this paper. The general results obtained in the paper are also valid for other types of parabolic equations with memory.Ecuaciones Diferenciales y Análisis Numérico2010info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/23670https://doi.org/10.1016/j.na.2010.03.012reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Analysis, 73(1), 183-201info:eu-repo/semantics/openAccessoai:idus.us.es:11441/236702026-06-17T12:51:07Z
dc.title.none.fl_str_mv Global attractor for a non-autonomous integro-differential equation in materials with memory
title Global attractor for a non-autonomous integro-differential equation in materials with memory
spellingShingle Global attractor for a non-autonomous integro-differential equation in materials with memory
Caraballo Garrido, Tomás
Delayed reaction-diffusion equations
integro-differential equations with memory
non-autonomous (pullback) attractors
multivalued dynamical systems
asymptotic behavior
title_short Global attractor for a non-autonomous integro-differential equation in materials with memory
title_full Global attractor for a non-autonomous integro-differential equation in materials with memory
title_fullStr Global attractor for a non-autonomous integro-differential equation in materials with memory
title_full_unstemmed Global attractor for a non-autonomous integro-differential equation in materials with memory
title_sort Global attractor for a non-autonomous integro-differential equation in materials with memory
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Garrido Atienza, María José
Schmalfuss, Björn
Valero Cuadra, José
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Garrido Atienza, María José
Schmalfuss, Björn
Valero Cuadra, José
author_role author
author2 Garrido Atienza, María José
Schmalfuss, Björn
Valero Cuadra, José
author2_role author
author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Delayed reaction-diffusion equations
integro-differential equations with memory
non-autonomous (pullback) attractors
multivalued dynamical systems
asymptotic behavior
topic Delayed reaction-diffusion equations
integro-differential equations with memory
non-autonomous (pullback) attractors
multivalued dynamical systems
asymptotic behavior
description The long-time behavior of an integro-differential parabolic equation of diffusion type with memory terms, expressed by convolution integrals involving infinite delays and by a forcing term with bounded delay, is investigated in this paper. The assumptions imposed on the coefficients are weak in the sense that uniqueness of solutions of the corresponding initial value problems cannot be guaranteed. Then, it is proved that the model generates a multivalued non–autonomous dynamical system which possesses a pullback attractor. First, the analysis is carried out with an abstract parabolic equation. Then, the theory is applied to the particular integro-differential equation which is the objective of this paper. The general results obtained in the paper are also valid for other types of parabolic equations with memory.
publishDate 2010
dc.date.none.fl_str_mv 2010
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/23670
https://doi.org/10.1016/j.na.2010.03.012
url http://hdl.handle.net/11441/23670
https://doi.org/10.1016/j.na.2010.03.012
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Analysis, 73(1), 183-201
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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