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

Let $\Omega$ 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 sugges...

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Detalles Bibliográficos
Autor: Rodríguez Bernal, Aníbal
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:20.500.14352/49706
Acceso en línea:https://hdl.handle.net/20.500.14352/49706
Access Level:acceso abierto
Palabra clave:517.9
Parabolic equations
Exponential type
Asymptotic behavior
Perturbations
Nonlinear perturbation
Linear perturbation
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equationsRodríguez Bernal, Aníbal517.9Parabolic equationsExponential typeAsymptotic behaviorPerturbationsNonlinear perturbationLinear perturbationEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasLet $\Omega$ 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.American Institute of Mathematical SciencesUniversidad Complutense de Madrid20092009-01-0120092009-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/49706reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/497062026-06-02T12:44:21Z
dc.title.none.fl_str_mv Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
title Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
spellingShingle Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
Rodríguez Bernal, Aníbal
517.9
Parabolic equations
Exponential type
Asymptotic behavior
Perturbations
Nonlinear perturbation
Linear perturbation
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
title_full Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
title_fullStr Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
title_full_unstemmed Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
title_sort Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
dc.creator.none.fl_str_mv Rodríguez Bernal, Aníbal
author Rodríguez Bernal, Aníbal
author_facet Rodríguez Bernal, Aníbal
author_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Parabolic equations
Exponential type
Asymptotic behavior
Perturbations
Nonlinear perturbation
Linear perturbation
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Parabolic equations
Exponential type
Asymptotic behavior
Perturbations
Nonlinear perturbation
Linear perturbation
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description Let $\Omega$ 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.
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/20.500.14352/49706
url https://hdl.handle.net/20.500.14352/49706
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 American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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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score 15.301603

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