Extremal equilibria for reaction-diffusion equations in bounded domains and applications

We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence an...

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Detalles Bibliográficos
Autores: Rodríguez Bernal, Aníbal, Vidal López, Alejandro
Tipo de recurso: artículo
Fecha de publicación:2008
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/49703
Acceso en línea:https://hdl.handle.net/20.500.14352/49703
Access Level:acceso abierto
Palabra clave:517.9
Reaction-diffusion equation
Extremal equilibria
Attractor
Nonlinear boundary conditions
Dirichlet boundary condition
Robin boundary condition
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
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spelling Extremal equilibria for reaction-diffusion equations in bounded domains and applicationsRodríguez Bernal, AníbalVidal López, Alejandro517.9Reaction-diffusion equationExtremal equilibriaAttractorNonlinear boundary conditionsDirichlet boundary conditionRobin boundary conditionEcuaciones diferenciales1202.07 Ecuaciones en DiferenciasWe show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equationElsevierUniversidad Complutense de Madrid20082008-01-0120082008-01-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/49703reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/497032026-06-02T12:44:21Z
dc.title.none.fl_str_mv Extremal equilibria for reaction-diffusion equations in bounded domains and applications
title Extremal equilibria for reaction-diffusion equations in bounded domains and applications
spellingShingle Extremal equilibria for reaction-diffusion equations in bounded domains and applications
Rodríguez Bernal, Aníbal
517.9
Reaction-diffusion equation
Extremal equilibria
Attractor
Nonlinear boundary conditions
Dirichlet boundary condition
Robin boundary condition
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
title_short Extremal equilibria for reaction-diffusion equations in bounded domains and applications
title_full Extremal equilibria for reaction-diffusion equations in bounded domains and applications
title_fullStr Extremal equilibria for reaction-diffusion equations in bounded domains and applications
title_full_unstemmed Extremal equilibria for reaction-diffusion equations in bounded domains and applications
title_sort Extremal equilibria for reaction-diffusion equations in bounded domains and applications
dc.creator.none.fl_str_mv Rodríguez Bernal, Aníbal
Vidal López, Alejandro
author Rodríguez Bernal, Aníbal
author_facet Rodríguez Bernal, Aníbal
Vidal López, Alejandro
author_role author
author2 Vidal López, Alejandro
author2_role author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.9
Reaction-diffusion equation
Extremal equilibria
Attractor
Nonlinear boundary conditions
Dirichlet boundary condition
Robin boundary condition
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
topic 517.9
Reaction-diffusion equation
Extremal equilibria
Attractor
Nonlinear boundary conditions
Dirichlet boundary condition
Robin boundary condition
Ecuaciones diferenciales
1202.07 Ecuaciones en Diferencias
description We show the existence of two special equilibria, the extremal ones, for a wide class of reaction–diffusion equations in bounded domains with several boundary conditions, including non-linear ones. They give bounds for the asymptotic dynamics and so for the attractor. Some results on the existence and/or uniqueness of positive solutions are also obtained. As a consequence, several well-known results on the existence and/or uniqueness of solutions for elliptic equations are revisited in a unified way obtaining, in addition, information on the dynamics of the associated parabolic problem. Finally, we ilustrate the use of the general results by applying them to the case of logistic equations. In fact, we obtain a detailed picture of the positive dynamics depending on the parameters appearing in the equation
publishDate 2008
dc.date.none.fl_str_mv 2008
2008-01-01
2008
2008-01-01
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/20.500.14352/49703
url https://hdl.handle.net/20.500.14352/49703
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 Elsevier
publisher.none.fl_str_mv Elsevier
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 15.300724

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