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Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations

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dc.contributor.authorRodríguez Bernal, Aníbal
dc.date.accessioned2023-06-20T09:29:25Z
dc.date.available2023-06-20T09:29:25Z
dc.date.issued2009
dc.description.abstractLet $\Omega$ be a bounded domain in a Euclidean space, with a smooth boundary. The paper deals with the linear non-autonomous model equation $$ u_t-\Delta u=C(t,x) \quad (x\in \Omega,\ t>0), $$ where $C(x,t)$ is a given function. Besides, various boundary conditions are imposed. The author suggests sharp qualitative and quantitative conditions to guarantee that the exponential type of the considered equation is modified by a linear perturbation. No assumption (periodic, almost periodic, quasi periodic etc.) is made on the time behavior of the coefficients of the equation or the perturbation. The obtained results are then applied to the investigation of the asymptotic behavior, both forwards and backwards, of solutions of certain nonautonomous nonlinear equations.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.sponsorshipMTM
dc.description.sponsorshipDGES and Programa de Financiación de Grupos de Investigación
dc.description.sponsorshipCADEDIF
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/12916
dc.identifier.doi10.3934/dcds.2009.25.1003
dc.identifier.issn1553-5231
dc.identifier.officialurlhttp://www.aimsciences.org/journals/dcdsA/online.jsp
dc.identifier.urihttps://hdl.handle.net/20.500.14352/49706
dc.issue.number3
dc.journal.titleDiscrete and Continuous Dynamical Systems. Series A.
dc.language.isoeng
dc.page.final1032
dc.page.initial1003
dc.publisherAmerican Institute of Mathematical Sciences
dc.relation.projectIDGR69/06
dc.relation.projectID2006–08262
dc.relation.projectIDGrupo 920894
dc.rights.accessRightsopen access
dc.subject.cdu517.9
dc.subject.keywordParabolic equations
dc.subject.keywordExponential type
dc.subject.keywordAsymptotic behavior
dc.subject.keywordPerturbations
dc.subject.keywordNonlinear perturbation
dc.subject.keywordLinear perturbation
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titlePerturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
dc.typejournal article
dc.volume.number25
dspace.entity.typePublication
relation.isAuthorOfPublicationfb7ac82c-5148-4dd1-b893-d8f8612a1b08
relation.isAuthorOfPublication.latestForDiscoveryfb7ac82c-5148-4dd1-b893-d8f8612a1b08
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