Singular solutions for space-time fractional equations in a bounded domain

This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular boundary data which are typical of fractional diffusion opera...

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Detalles Bibliográficos
Autores: Chan, Hardy, Gómez Castro, David, Vázquez, Juan Luis
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/73324
Acceso en línea:https://hdl.handle.net/20.500.14352/73324
Access Level:acceso abierto
Palabra clave:517.95
Analysis of PDEs
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
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spelling Singular solutions for space-time fractional equations in a bounded domainChan, HardyGómez Castro, DavidVázquez, Juan Luis517.95Analysis of PDEsAnálisis matemáticoEcuaciones diferenciales1202 Análisis y Análisis Funcional1202.07 Ecuaciones en DiferenciasThis paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular boundary data which are typical of fractional diffusion operators in space, and the other one is the consideration of the fractional-in-time Caputo and Riemann-Liouville derivatives in a unified way. We first construct classical solutions of our problems using the spectral theory and discussing the corresponding fractional-in-time ordinary differential equations. We take advantage of the duality between these fractional-in-time derivatives to introduce the notion of weak-dual solution for weighted-integrable data. As the main result of the paper, we prove the well-posedness of the initial and boundary-value problems in this sense.Universidad Complutense de Madrid20232023-04-1120232023-04-11journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/20.500.14352/73324reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/733242026-06-02T12:44:21Z
dc.title.none.fl_str_mv Singular solutions for space-time fractional equations in a bounded domain
title Singular solutions for space-time fractional equations in a bounded domain
spellingShingle Singular solutions for space-time fractional equations in a bounded domain
Chan, Hardy
517.95
Analysis of PDEs
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
title_short Singular solutions for space-time fractional equations in a bounded domain
title_full Singular solutions for space-time fractional equations in a bounded domain
title_fullStr Singular solutions for space-time fractional equations in a bounded domain
title_full_unstemmed Singular solutions for space-time fractional equations in a bounded domain
title_sort Singular solutions for space-time fractional equations in a bounded domain
dc.creator.none.fl_str_mv Chan, Hardy
Gómez Castro, David
Vázquez, Juan Luis
author Chan, Hardy
author_facet Chan, Hardy
Gómez Castro, David
Vázquez, Juan Luis
author_role author
author2 Gómez Castro, David
Vázquez, Juan Luis
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517.95
Analysis of PDEs
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
topic 517.95
Analysis of PDEs
Análisis matemático
Ecuaciones diferenciales
1202 Análisis y Análisis Funcional
1202.07 Ecuaciones en Diferencias
description This paper is devoted to describing a linear diffusion problem involving fractional-in-time derivatives and self-adjoint integro-differential space operators posed in bounded domains. One main concern of our paper is to deal with singular boundary data which are typical of fractional diffusion operators in space, and the other one is the consideration of the fractional-in-time Caputo and Riemann-Liouville derivatives in a unified way. We first construct classical solutions of our problems using the spectral theory and discussing the corresponding fractional-in-time ordinary differential equations. We take advantage of the duality between these fractional-in-time derivatives to introduce the notion of weak-dual solution for weighted-integrable data. As the main result of the paper, we prove the well-posedness of the initial and boundary-value problems in this sense.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023-04-11
2023
2023-04-11
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/20.500.14352/73324
url https://hdl.handle.net/20.500.14352/73324
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.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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