Dynamics in dumbbell domains III. Continuity of attractors

In this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic f...

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Detalles Bibliográficos
Autores: Arrieta Algarra, José María, Carvalho, Alexandre N., Lozada-Cruz, Germán
Tipo de recurso: artículo
Fecha de publicación:2009
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/42008
Acceso en línea:https://hdl.handle.net/20.500.14352/42008
Access Level:acceso abierto
Palabra clave:517.9
Hyperbolic equilibria
Shrinking channels
Lower semicontinuous
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Dynamics in dumbbell domains III. Continuity of attractorsArrieta Algarra, José MaríaCarvalho, Alexandre N.Lozada-Cruz, Germán517.9Hyperbolic equilibriaShrinking channelsLower semicontinuousEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasIn this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [4], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in Lp and H1 normsElsevierUniversidad Complutense de Madrid20092009-01-0120092009-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/42008reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/420082026-06-02T12:44:21Z
dc.title.none.fl_str_mv Dynamics in dumbbell domains III. Continuity of attractors
title Dynamics in dumbbell domains III. Continuity of attractors
spellingShingle Dynamics in dumbbell domains III. Continuity of attractors
Arrieta Algarra, José María
517.9
Hyperbolic equilibria
Shrinking channels
Lower semicontinuous
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Dynamics in dumbbell domains III. Continuity of attractors
title_full Dynamics in dumbbell domains III. Continuity of attractors
title_fullStr Dynamics in dumbbell domains III. Continuity of attractors
title_full_unstemmed Dynamics in dumbbell domains III. Continuity of attractors
title_sort Dynamics in dumbbell domains III. Continuity of attractors
dc.creator.none.fl_str_mv Arrieta Algarra, José María
Carvalho, Alexandre N.
Lozada-Cruz, Germán
author Arrieta Algarra, José María
author_facet Arrieta Algarra, José María
Carvalho, Alexandre N.
Lozada-Cruz, Germán
author_role author
author2 Carvalho, Alexandre N.
Lozada-Cruz, Germán
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Hyperbolic equilibria
Shrinking channels
Lower semicontinuous
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Hyperbolic equilibria
Shrinking channels
Lower semicontinuous
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description In this paper we conclude the analysis started in [3] and continued in [4] con- cerning the behavior of the asymptotic dynamics of a dissipative reactions di_usion equation in a dumbbell domain as the channel shrinks to a line segment. In [3], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [4], we have analyzed the behavior of the limiting problem. In this paper we show that the attractors are upper semicontinuous and, moreover, if all equilibria of the limiting problem are hyperbolic, then they are lower semicontinuous and therefore, continuous. The continuity is obtained in Lp and H1 norms
publishDate 2009
dc.date.none.fl_str_mv 2009
2009-01-01
2009
2009-01-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/42008
url https://hdl.handle.net/20.500.14352/42008
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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