Non-Autonomous Attractor for Integro-Differential Evolution Equations

We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an infinite delay. Moreover, when conditions guaranteeing uniqueness of solutions do...

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Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Kloeden, Peter E.
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:11441/23682
Acceso en línea:http://hdl.handle.net/11441/23682
https://doi.org/10.3934/dcdss.2009.2.17
Access Level:acceso abierto
Palabra clave:Integro-differential equation
differential equation with infinite delay
set-valued process
set-valued non-autonomous dynamical system
pullback attractor
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spelling Non-Autonomous Attractor for Integro-Differential Evolution EquationsCaraballo Garrido, TomásKloeden, Peter E.Integro-differential equationdifferential equation with infinite delayset-valued processset-valued non-autonomous dynamical systempullback attractorWe show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an infinite delay. Moreover, when conditions guaranteeing uniqueness of solutions do not hold, they generate a non-autonomous (possibly) multi-valued dynamical system (MNDS). The pullback attractors here are defined with respect to a universe of subsets of the state space with sub-exponetial growth, rather than restricted to bounded sets. The theory of non-autonomous pullback attractors is extended to such MNDS in a general setting and then applied to the original integro-differential equations. Examples based on the logistic equations with and without a diffusion term are considered.Ecuaciones Diferenciales y Análisis Numérico2009info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/23682https://doi.org/10.3934/dcdss.2009.2.17reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésDiscrete and Continuous Dynamical Systems. Series S, 2(1), 17-36info:eu-repo/semantics/openAccessoai:idus.us.es:11441/236822026-06-17T12:51:07Z
dc.title.none.fl_str_mv Non-Autonomous Attractor for Integro-Differential Evolution Equations
title Non-Autonomous Attractor for Integro-Differential Evolution Equations
spellingShingle Non-Autonomous Attractor for Integro-Differential Evolution Equations
Caraballo Garrido, Tomás
Integro-differential equation
differential equation with infinite delay
set-valued process
set-valued non-autonomous dynamical system
pullback attractor
title_short Non-Autonomous Attractor for Integro-Differential Evolution Equations
title_full Non-Autonomous Attractor for Integro-Differential Evolution Equations
title_fullStr Non-Autonomous Attractor for Integro-Differential Evolution Equations
title_full_unstemmed Non-Autonomous Attractor for Integro-Differential Evolution Equations
title_sort Non-Autonomous Attractor for Integro-Differential Evolution Equations
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Kloeden, Peter E.
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Kloeden, Peter E.
author_role author
author2 Kloeden, Peter E.
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Integro-differential equation
differential equation with infinite delay
set-valued process
set-valued non-autonomous dynamical system
pullback attractor
topic Integro-differential equation
differential equation with infinite delay
set-valued process
set-valued non-autonomous dynamical system
pullback attractor
description We show that infinite-dimensional integro-differential equations which involve an integral of the solution over the time interval since starting can be formulated as non-autonomous delay differential equations with an infinite delay. Moreover, when conditions guaranteeing uniqueness of solutions do not hold, they generate a non-autonomous (possibly) multi-valued dynamical system (MNDS). The pullback attractors here are defined with respect to a universe of subsets of the state space with sub-exponetial growth, rather than restricted to bounded sets. The theory of non-autonomous pullback attractors is extended to such MNDS in a general setting and then applied to the original integro-differential equations. Examples based on the logistic equations with and without a diffusion term are considered.
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/11441/23682
https://doi.org/10.3934/dcdss.2009.2.17
url http://hdl.handle.net/11441/23682
https://doi.org/10.3934/dcdss.2009.2.17
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Discrete and Continuous Dynamical Systems. Series S, 2(1), 17-36
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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