Dynamics in dumbbell domains III. Continuity of attractors

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dc.contributor.authorArrieta, Jose M.
dc.contributor.authorCarvalho, Alexandre N.
dc.contributor.authorLozada-Cruz, German Jesus [UNESP]
dc.contributor.institutionUniv Complutense Madrid
dc.contributor.institutionUniversidade de São Paulo (USP)
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T15:34:18Z
dc.date.available2014-05-20T15:34:18Z
dc.date.issued2009-07-01
dc.description.abstractIn this paper we conclude the analysis started in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597] and continued in [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz, Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)] concerning the behavior of the asymptotic dynamics of a dissipative reaction-diffusion equation in a dumbbell domain as the channel shrinks to a line segment. In [J.M. Arrieta, AN Carvalho. G. Lozada-Cruz, Dynamics in dumbbell domains I. Continuity of the set of equilibria, J. Differential Equations 231 (2006) 551-597], we have established an appropriate functional analytic framework to address this problem and we have shown the continuity of the set of equilibria. In [J.M. Arrieta, AN Carvalho, G. Lozada-Cruz. Dynamics in dumbbell domains II. The limiting problem, J. Differential Equations 247 (1) (2009) 174-202 (this issue)], 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 L(p) and H(1) norms. (C) 2008 Elsevier B.V. All rights reserved.en
dc.description.affiliationUniv Complutense Madrid, Dept Matemat Aplicada, Fac Matemat, E-28040 Madrid, Spain
dc.description.affiliationUniv São Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, BR-13560970 São Carlos, SP, Brazil
dc.description.affiliationUniv Estadual Paulista, Dept Matemat, IBILCE, UNESP, BR-15054000 Sao Jose Dos Campos, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Dept Matemat, IBILCE, UNESP, BR-15054000 Sao Jose Dos Campos, Brazil
dc.description.sponsorshipMEC
dc.description.sponsorshipPrograma de Financiacion de Grupos de Investigacion UCM-Comunidad de Madrid
dc.description.sponsorshipSIMUMAT-Comunidad de Madrid, Spain
dc.description.sponsorshipConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
dc.description.sponsorshipCoordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
dc.description.sponsorshipFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
dc.description.sponsorshipIdMEC: PHB2006-003-PC
dc.description.sponsorshipIdMEC: MTM2006-08262
dc.description.sponsorshipIdPrograma de Financiacion de Grupos de Investigacion UCM-Comunidad de Madrid: CCG07-UCM/ESP-2393
dc.description.sponsorshipIdPrograma de Financiacion de Grupos de Investigacion UCM-Comunidad de Madrid: 920894
dc.description.sponsorshipIdCNPq: 305447/2005-0
dc.description.sponsorshipIdCNPq: 451761/2008-1
dc.description.sponsorshipIdCAPES: 267/2008
dc.description.sponsorshipIdFAPESP: 08/53094-4
dc.description.sponsorshipIdFAPESP: 06/04781-3
dc.description.sponsorshipIdFAPESP: 07/100981-0
dc.format.extent225-259
dc.identifierhttp://dx.doi.org/10.1016/j.jde.2008.12.014
dc.identifier.citationJournal of Differential Equations. San Diego: Academic Press Inc. Elsevier B.V., v. 247, n. 1, p. 225-259, 2009.
dc.identifier.doi10.1016/j.jde.2008.12.014
dc.identifier.fileWOS000266256900010.pdf
dc.identifier.issn0022-0396
dc.identifier.lattes9125376680065204
dc.identifier.urihttp://hdl.handle.net/11449/42494
dc.identifier.wosWOS:000266256900010
dc.language.isoeng
dc.publisherAcademic Press Inc. Elsevier B.V.
dc.relation.ispartofJournal of Differential Equations
dc.relation.ispartofjcr1.782
dc.relation.ispartofsjr2,525
dc.rights.accessRightsAcesso aberto
dc.sourceWeb of Science
dc.titleDynamics in dumbbell domains III. Continuity of attractorsen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderAcademic Press Inc. Elsevier B.V.
unesp.author.lattes9125376680065204
unesp.author.orcid0000-0002-9274-5039[1]
unesp.author.orcid0000-0003-2860-954X[3]
unesp.author.orcid0000-0003-4279-6740[2]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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Artigos - Matemática - IBILCE