Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions

In this paper, we prove some regularity results for pullback attractors of a non-autonomous reaction–diffusion model with dynamical boundary conditions considered in Anguiano (2011). Under certain assumptions of the nonlinear terms we show a regularity result for the unique solution of the problem....

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Authors: Anguiano Moreno, María, Marín Rubio, Pedro, Real Anguas, José
Format: article
Status:Versión enviada para evaluación y publicación
Publication Date:2014
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/25952
Online Access:http://hdl.handle.net/11441/25952
https://doi.org/10.1016/j.nonrwa.2014.05.003
Access Level:Open access
Keyword:Reaction–diffusion equations
Dynamical boundary conditions
Pullback attractors
Tempered exponential growth
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spelling Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary ConditionsAnguiano Moreno, MaríaMarín Rubio, PedroReal Anguas, JoséReaction–diffusion equationsDynamical boundary conditionsPullback attractorsTempered exponential growthIn this paper, we prove some regularity results for pullback attractors of a non-autonomous reaction–diffusion model with dynamical boundary conditions considered in Anguiano (2011). Under certain assumptions of the nonlinear terms we show a regularity result for the unique solution of the problem. We establish a general result about boundedness of invariant sets for the associated evolution process in the norm of the domain of the spatial linear operator appearing in the equation. As a consequence, we deduce that the pullback attractors of the model are bounded in this domain norm. After that, under additional assumptions, some exponential growth results for pullback attractors when time goes to −∞ are proved.ElsevierEcuaciones Diferenciales y Análisis Numérico2014info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/25952https://doi.org/10.1016/j.nonrwa.2014.05.003reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésNonlinear Analysis: Real World Applications, 112-125info:eu-repo/semantics/openAccessoai:idus.us.es:11441/259522026-06-17T12:51:07Z
dc.title.none.fl_str_mv Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
title Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
spellingShingle Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
Anguiano Moreno, María
Reaction–diffusion equations
Dynamical boundary conditions
Pullback attractors
Tempered exponential growth
title_short Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
title_full Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
title_fullStr Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
title_full_unstemmed Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
title_sort Regularity Results and Exponential Growth for Pullback Attractors of a Non-Autonomous Reaction-Diffusion Model with Dynamical Boundary Conditions
dc.creator.none.fl_str_mv Anguiano Moreno, María
Marín Rubio, Pedro
Real Anguas, José
author Anguiano Moreno, María
author_facet Anguiano Moreno, María
Marín Rubio, Pedro
Real Anguas, José
author_role author
author2 Marín Rubio, Pedro
Real Anguas, José
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
dc.subject.none.fl_str_mv Reaction–diffusion equations
Dynamical boundary conditions
Pullback attractors
Tempered exponential growth
topic Reaction–diffusion equations
Dynamical boundary conditions
Pullback attractors
Tempered exponential growth
description In this paper, we prove some regularity results for pullback attractors of a non-autonomous reaction–diffusion model with dynamical boundary conditions considered in Anguiano (2011). Under certain assumptions of the nonlinear terms we show a regularity result for the unique solution of the problem. We establish a general result about boundedness of invariant sets for the associated evolution process in the norm of the domain of the spatial linear operator appearing in the equation. As a consequence, we deduce that the pullback attractors of the model are bounded in this domain norm. After that, under additional assumptions, some exponential growth results for pullback attractors when time goes to −∞ are proved.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11441/25952
https://doi.org/10.1016/j.nonrwa.2014.05.003
url http://hdl.handle.net/11441/25952
https://doi.org/10.1016/j.nonrwa.2014.05.003
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Nonlinear Analysis: Real World Applications, 112-125
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:idUS. Depósito de Investigación de la Universidad de Sevilla
instname:Universidad de Sevilla (US)
instname_str Universidad de Sevilla (US)
reponame_str idUS. Depósito de Investigación de la Universidad de Sevilla
collection idUS. Depósito de Investigación de la Universidad de Sevilla
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300719

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