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Dynamics in dumbbell domains III. Continuity of attractors

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dc.contributor.authorArrieta Algarra, José María
dc.contributor.authorCarvalho, Alexandre N.
dc.contributor.authorLozada-Cruz, Germán
dc.date.accessioned2023-06-20T00:07:03Z
dc.date.available2023-06-20T00:07:03Z
dc.date.issued2009
dc.description.abstractIn 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
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMEC
dc.description.sponsorshipPrograma de Financiaci_on de Grupos de Investigaci_on UCM-Comunidad de Madrid CCG07-UCM/ESP-2393. Grupo 920894
dc.description.sponsorshipSIMUMAT-Comunidad de Madrid
dc.description.sponsorshipCNPq
dc.description.sponsorshipCAPES/DGU
dc.description.sponsorshipFAPESP
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/13945
dc.identifier.doi10.1016/j.jde.2008.12.014
dc.identifier.issn0022-0396
dc.identifier.officialurlhttp://www.sciencedirect.com/science/journal/00220396
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42008
dc.issue.number1
dc.journal.titleJournal of Differential Equations
dc.language.isoeng
dc.page.final259
dc.page.initial225
dc.publisherElsevier
dc.relation.projectIDPHB2006-003-PC
dc.relation.projectIDMTM2006-08262
dc.relation.projectID305447/2005-0
dc.relation.projectID451761/2008-1
dc.relation.projectID2008/53094-4
dc.relation.projectID06/04781-3
dc.relation.projectID07/00981-0
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.keywordHyperbolic equilibria
dc.subject.keywordShrinking channels
dc.subject.keywordLower semicontinuous
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleDynamics in dumbbell domains III. Continuity of attractors
dc.typejournal article
dc.volume.number247
dspace.entity.typePublication
relation.isAuthorOfPublication2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a
relation.isAuthorOfPublication.latestForDiscovery2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a

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