Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations

In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They rst prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satis e...

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Autores: Zhao, Caidi, Caraballo Garrido, Tomás, Lukaszewicz, Grzegorz
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2021
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/106412
Acceso en línea:https://hdl.handle.net/11441/106412
https://doi.org/10.1016/j.jde.2021.01.039
Access Level:acceso abierto
Palabra clave:Klein-Gordon-Schdinger equations
Statistical solution
Pullback attractor
Invariant measure
Liouville type theorem
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spelling Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equationsZhao, CaidiCaraballo Garrido, TomásLukaszewicz, GrzegorzKlein-Gordon-Schdinger equationsStatistical solutionPullback attractorInvariant measureLiouville type theoremIn this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They rst prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satis es a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem.Ministerio de Ciencia e Innovación (MCIU). España PGC2018-096540-B-I00Agencia Estatal de Investigación (AEI). España PGC2018-096540-B-I00Fondo Europeo de Desarrollo Regional (FEDER) PGC2018-096540-B-I00Elsevier [Commercial Publisher], Academic Press [Associate Organisation]Ecuaciones Diferenciales y Análisis NuméricoFQM314: Análisis Estocástico de Sistemas DiferencialesMinisterio de Ciencia, Innovación y Universidades (MCIU). EspañaAgencia Estatal de Investigación. EspañaEuropean Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)2021info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfapplication/pdfhttps://hdl.handle.net/11441/106412https://doi.org/10.1016/j.jde.2021.01.039reponame:idUS. Depósito de Investigación de la Universidad de Sevillainstname:Universidad de Sevilla (US)InglésJournal of Differential Equations, 281 (April), 1-1-32-32.PGC2018-096540-B-I00https://doi.org/10.1016/j.jde.2021.01.039info:eu-repo/semantics/openAccessoai:idus.us.es:11441/1064122026-06-17T12:51:07Z
dc.title.none.fl_str_mv Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
title Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
spellingShingle Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
Zhao, Caidi
Klein-Gordon-Schdinger equations
Statistical solution
Pullback attractor
Invariant measure
Liouville type theorem
title_short Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
title_full Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
title_fullStr Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
title_full_unstemmed Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
title_sort Statistical solution and Liouville type theorem for the Klein-Gordon-Schrödinger equations
dc.creator.none.fl_str_mv Zhao, Caidi
Caraballo Garrido, Tomás
Lukaszewicz, Grzegorz
author Zhao, Caidi
author_facet Zhao, Caidi
Caraballo Garrido, Tomás
Lukaszewicz, Grzegorz
author_role author
author2 Caraballo Garrido, Tomás
Lukaszewicz, Grzegorz
author2_role author
author
dc.contributor.none.fl_str_mv Ecuaciones Diferenciales y Análisis Numérico
FQM314: Análisis Estocástico de Sistemas Diferenciales
Ministerio de Ciencia, Innovación y Universidades (MCIU). España
Agencia Estatal de Investigación. España
European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
dc.subject.none.fl_str_mv Klein-Gordon-Schdinger equations
Statistical solution
Pullback attractor
Invariant measure
Liouville type theorem
topic Klein-Gordon-Schdinger equations
Statistical solution
Pullback attractor
Invariant measure
Liouville type theorem
description In this article, the authors investigate the system of Schr odinger and Klein-Gordon equations with Yukawa coupling. They rst prove the existence of pullback attractor and construct a family of invariant Borel probability measures. Then they establish that this family of probability measures satis es a Liouville type theorem and is indeed a statistical solution for the coupling equations. Further, they reveal that the invariant property of the statistical solution is a particular situation of the Liouville type theorem.
publishDate 2021
dc.date.none.fl_str_mv 2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/11441/106412
https://doi.org/10.1016/j.jde.2021.01.039
url https://hdl.handle.net/11441/106412
https://doi.org/10.1016/j.jde.2021.01.039
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Journal of Differential Equations, 281 (April), 1-1-32-32.
PGC2018-096540-B-I00
https://doi.org/10.1016/j.jde.2021.01.039
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 [Commercial Publisher], Academic Press [Associate Organisation]
publisher.none.fl_str_mv Elsevier [Commercial Publisher], Academic Press [Associate Organisation]
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 15,301603

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