Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay

This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the problem, and a result ensuring the existence and uniqueness of mild solutions...

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Detalles Bibliográficos
Autores: Xu, Jiaohui, Zhang, Zhengce, Caraballo Garrido, Tomás
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2019
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/85591
Acceso en línea:https://hdl.handle.net/11441/85591
Access Level:acceso abierto
Palabra clave:Impulsive fractional stochastic evolution equations
Infinite delay
Mild solutions
Global forward attracting set
Singleton
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spelling Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delayXu, JiaohuiZhang, ZhengceCaraballo Garrido, TomásImpulsive fractional stochastic evolution equationsInfinite delayMild solutionsGlobal forward attracting setSingletonThis paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the problem, and a result ensuring the existence and uniqueness of mild solutions globally defined in future, the existence of a minimal global attracting set is investigated in the mean-square topology, under general assumptions not ensuing the uniqueness of solutions. Furthermore, in the case of uniqueness, it is possible to provide more information about the geometrical structure of such global attracting set. In particular, it is proved that the minimal compact globally attracting set for the solutions of the problem becomes a singleton. It is remarkable that the attraction property is proved in the usual forward sense, unlike the pullback concept used in the context of random dynamical systems, but the main point is that the model under study has not been proved to generate a random dynamical system.National Natural Science Foundation of ChinaFondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y CompetitividadConsejería de Innovación, Ciencia y Empresa (Junta de Andalucía)ElsevierEcuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas Diferenciales2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/85591reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésCommunications in Nonlinear Science and Numerical Simulation, 75, 121-139.11371286MTM2015-63723-PP12-FQM-1492https://reader.elsevier.com/reader/sd/pii/S100757041930070X?token=E8E17F42A4485070BB65D93E7573A60F6B8F2178C8F3428EEA0E7F419623E7B5515F8221C053A1945D15D056062BC6E5info:eu-repo/semantics/openAccessoai:idus.us.es:11441/855912026-06-17T12:51:07Z
dc.title.none.fl_str_mv Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
title Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
spellingShingle Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
Xu, Jiaohui
Impulsive fractional stochastic evolution equations
Infinite delay
Mild solutions
Global forward attracting set
Singleton
title_short Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
title_full Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
title_fullStr Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
title_full_unstemmed Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
title_sort Well-posedness and dynamics of impulsive fractional stochastic evolution equations with unbounded delay
dc.creator.none.fl_str_mv Xu, Jiaohui
Zhang, Zhengce
Caraballo Garrido, Tomás
author Xu, Jiaohui
author_facet Xu, Jiaohui
Zhang, Zhengce
Caraballo Garrido, Tomás
author_role author
author2 Zhang, Zhengce
Caraballo Garrido, Tomás
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 Impulsive fractional stochastic evolution equations
Infinite delay
Mild solutions
Global forward attracting set
Singleton
topic Impulsive fractional stochastic evolution equations
Infinite delay
Mild solutions
Global forward attracting set
Singleton
description This paper is concerned with the well-posedness and dynamics of delay impulsive fractional stochastic evolution equations with time fractional differential operator α ∈ (0, 1). After establishing the well-posedness of the problem, and a result ensuring the existence and uniqueness of mild solutions globally defined in future, the existence of a minimal global attracting set is investigated in the mean-square topology, under general assumptions not ensuing the uniqueness of solutions. Furthermore, in the case of uniqueness, it is possible to provide more information about the geometrical structure of such global attracting set. In particular, it is proved that the minimal compact globally attracting set for the solutions of the problem becomes a singleton. It is remarkable that the attraction property is proved in the usual forward sense, unlike the pullback concept used in the context of random dynamical systems, but the main point is that the model under study has not been proved to generate a random dynamical system.
publishDate 2019
dc.date.none.fl_str_mv 2019
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 https://hdl.handle.net/11441/85591
url https://hdl.handle.net/11441/85591
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Communications in Nonlinear Science and Numerical Simulation, 75, 121-139.
11371286
MTM2015-63723-P
P12-FQM-1492
https://reader.elsevier.com/reader/sd/pii/S100757041930070X?token=E8E17F42A4485070BB65D93E7573A60F6B8F2178C8F3428EEA0E7F419623E7B5515F8221C053A1945D15D056062BC6E5
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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