On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems

For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefu...

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Detalhes bibliográficos
Autores: Marín Rubio, Pedro, Real Anguas, José
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2009
País:España
Recursos:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25936
Acesso em linha:http://hdl.handle.net/11441/25936
https://doi.org/10.1016/j.na.2009.02.065
Access Level:acceso abierto
Palavra-chave:Pullback attractors
Non-autonomous dynamical systems
Tempered sets
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spelling On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical SystemsMarín Rubio, PedroReal Anguas, JoséPullback attractorsNon-autonomous dynamical systemsTempered setsFor an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier–Stokes model, improving some previous results on attractor theory.ElsevierEcuaciones Diferenciales y Análisis Numérico2009info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/25936https://doi.org/10.1016/j.na.2009.02.065reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear analysis: Theory, methods & applications, 71(9), 3956-3963http://dx.doi.org/10.1016/j.na.2009.02.065info:eu-repo/semantics/openAccessoai:idus.us.es:11441/259362026-06-17T12:51:07Z
dc.title.none.fl_str_mv On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
title On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
spellingShingle On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
Marín Rubio, Pedro
Pullback attractors
Non-autonomous dynamical systems
Tempered sets
title_short On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
title_full On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
title_fullStr On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
title_full_unstemmed On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
title_sort On The Relation Between Two Different Concepts of Pullback Attractors for Non-Autonomous Dynamical Systems
dc.creator.none.fl_str_mv Marín Rubio, Pedro
Real Anguas, José
author Marín Rubio, Pedro
author_facet Marín Rubio, Pedro
Real Anguas, José
author_role author
author2 Real Anguas, José
author2_role author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Pullback attractors
Non-autonomous dynamical systems
Tempered sets
topic Pullback attractors
Non-autonomous dynamical systems
Tempered sets
description For an abstract dynamical system, we establish, under minimal assumptions, the existence of D-attractor, i.e. a pullback attractor for a given class D of families of time varying subsets of the phase space. We relate this concept with the usual attractor of fixed bounded sets, pointing out its usefulness in order to ensure the existence of this last attractor in particular situations. Moreover, we prove that under a simple assumption these two notions of attractors generate, in fact, the same object. This is then applied to a Navier–Stokes model, improving some previous results on attractor theory.
publishDate 2009
dc.date.none.fl_str_mv 2009
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/25936
https://doi.org/10.1016/j.na.2009.02.065
url http://hdl.handle.net/11441/25936
https://doi.org/10.1016/j.na.2009.02.065
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear analysis: Theory, methods & applications, 71(9), 3956-3963
http://dx.doi.org/10.1016/j.na.2009.02.065
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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