Publication:
Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

dc.contributor.authorArrieta Algarra, José María
dc.contributor.authorCarvalho, Alexandre N.
dc.contributor.authorLanga, José A.
dc.contributor.authorRodríguez Bernal, Aníbal
dc.date.accessioned2023-06-20T00:17:42Z
dc.date.available2023-06-20T00:17:42Z
dc.date.issued2012-09
dc.description.abstractIn this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMICINN
dc.description.sponsorshipUCM-BCSH
dc.description.sponsorshipMICINN
dc.description.sponsorshipCNPq
dc.description.sponsorshipFAFESP, Brazil
dc.description.sponsorshipFEDER, Spain
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/16761
dc.identifier.doi10.1007/s10884-012-9269-y
dc.identifier.issn1040-7294
dc.identifier.officialurlhttp://www.springerlink.com/content/1411835408267004/fulltext.pdf
dc.identifier.relatedurlhttp://www.springerlink.com/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/42346
dc.issue.number3
dc.journal.titleJournal of Dynamics and Differential Equations
dc.language.isoeng
dc.page.final481
dc.page.initial427
dc.publisherSpringer
dc.relation.projectIDMTM2009-07540
dc.relation.projectIDGR35/10-A Grupo 920894
dc.relation.projectIDPHB2006-0003-PC
dc.relation.projectIDPBH2006-0003-PC
dc.relation.projectIDMTM2008-00088
dc.relation.projectIDMTM2011-22411
dc.relation.projectID305447/2005-0
dc.relation.projectID03/10042-0
dc.relation.projectIDPBH2006-0003-PC
dc.relation.projectIDMTM2008-00088
dc.relation.projectIDMTM2011-22411
dc.relation.projectIDHF2008-0039
dc.rights.accessRightsrestricted access
dc.subject.cdu517.9
dc.subject.keywordNonautonomous dynamical systems
dc.subject.keywordHyperbolic global bounded solutions
dc.subject.keywordUnstable manifolds
dc.subject.keywordDichotomy
dc.subject.keywordSingular perturbations
dc.subject.keywordAttractors
dc.subject.keywordLower semicontinuity
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleContinuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations
dc.typejournal article
dc.volume.number24
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a
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