Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems

In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion type. Firstly, we prove the existence of weak solutions making use of a change...

Descripción completa

Detalles Bibliográficos
Autores: Caraballo Garrido, Tomás, Herrera Cobos, Marta, Marín Rubio, Pedro
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2018
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/67409
Acceso en línea:http://hdl.handle.net/11441/67409
https://doi.org/10.1016/j.jmaa.2017.11.013
Access Level:acceso abierto
Palabra clave:Nonlocal p-Laplacian equations
Pullback attractors
Asymptotic compactness
Multi-valued dynamical systems
id ES_ce7456ba9f2ff58e54bbaccd9acb07c8
oai_identifier_str oai:idus.us.es:11441/67409
network_acronym_str ES
network_name_str España
repository_id_str
spelling Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problemsCaraballo Garrido, TomásHerrera Cobos, MartaMarín Rubio, PedroNonlocal p-Laplacian equationsPullback attractorsAsymptotic compactnessMulti-valued dynamical systemsIn this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion type. Firstly, we prove the existence of weak solutions making use of a change of variable which allows us to get rid of the nonlocal operator in the diffusion term. Thereupon, the regularising effect of the equation is shown applying an argument of a posteriori regularity, since under the assumptions made we cannot guarantee the uniqueness of weak solutions. In addition, this argument allows to ensure the existence of an absorbing family in W1,p 0 (Ω). This leads to the existence of the minimal pullback attractors in L2(Ω), Lp(Ω) and some other spaces as Lp∗−(Ω). Relationships between these families are also established.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de AndalucíaElsevierEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttp://hdl.handle.net/11441/67409https://doi.org/10.1016/j.jmaa.2017.11.013reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Mathematical Analysis and Applications, 459 (2), 997-1015.MTM2015-63723-PP12-FQM-1492BES-2012-053398https://ac.els-cdn.com/S0022247X17310144/1-s2.0-S0022247X17310144-main.pdf?_tid=c870c86a-de58-11e7-a44c-00000aacb361&acdnat=1512986036_ad64f206e62be1357ab7ddc81a5a1ba7info:eu-repo/semantics/openAccessoai:idus.us.es:11441/674092026-06-17T12:51:07Z
dc.title.none.fl_str_mv Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
title Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
spellingShingle Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
Caraballo Garrido, Tomás
Nonlocal p-Laplacian equations
Pullback attractors
Asymptotic compactness
Multi-valued dynamical systems
title_short Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
title_full Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
title_fullStr Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
title_full_unstemmed Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
title_sort Asymptotic behaviour of nonlocal p-Laplacian reaction-diffusion problems
dc.creator.none.fl_str_mv Caraballo Garrido, Tomás
Herrera Cobos, Marta
Marín Rubio, Pedro
author Caraballo Garrido, Tomás
author_facet Caraballo Garrido, Tomás
Herrera Cobos, Marta
Marín Rubio, Pedro
author_role author
author2 Herrera Cobos, Marta
Marín Rubio, Pedro
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
dc.subject.none.fl_str_mv Nonlocal p-Laplacian equations
Pullback attractors
Asymptotic compactness
Multi-valued dynamical systems
topic Nonlocal p-Laplacian equations
Pullback attractors
Asymptotic compactness
Multi-valued dynamical systems
description In this paper, we focus on studying the existence of attractors in the phase spaces L2(Ω) and Lp(Ω) (among others) for time-dependent p-Laplacian equations with nonlocal diffusion and nonlinearities of reaction-diffusion type. Firstly, we prove the existence of weak solutions making use of a change of variable which allows us to get rid of the nonlocal operator in the diffusion term. Thereupon, the regularising effect of the equation is shown applying an argument of a posteriori regularity, since under the assumptions made we cannot guarantee the uniqueness of weak solutions. In addition, this argument allows to ensure the existence of an absorbing family in W1,p 0 (Ω). This leads to the existence of the minimal pullback attractors in L2(Ω), Lp(Ω) and some other spaces as Lp∗−(Ω). Relationships between these families are also established.
publishDate 2018
dc.date.none.fl_str_mv 2018
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/11441/67409
https://doi.org/10.1016/j.jmaa.2017.11.013
url http://hdl.handle.net/11441/67409
https://doi.org/10.1016/j.jmaa.2017.11.013
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Mathematical Analysis and Applications, 459 (2), 997-1015.
MTM2015-63723-P
P12-FQM-1492
BES-2012-053398
https://ac.els-cdn.com/S0022247X17310144/1-s2.0-S0022247X17310144-main.pdf?_tid=c870c86a-de58-11e7-a44c-00000aacb361&acdnat=1512986036_ad64f206e62be1357ab7ddc81a5a1ba7
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
_version_ 1869419992672370688
score 15.300724

Similares en LA Referencia