On decay rates of the solutions of parabolic Cauchy problems

[EN] We consider the Cauchy problem for a general class of parabolic partial differential equations in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast growing weight w, there is a Schauder basis (e(n))(n=1)(infinity) in L-w...

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Detalles Bibliográficos
Autores: Bonet Solves, José Antonio|||0000-0002-9096-6380, Lusky, Wolfgang, Taskinen, Jari
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/189475
Acceso en línea:https://riunet.upv.es/handle/10251/189475
Access Level:acceso abierto
Palabra clave:Parabolic PDE
Cauchy problem
Banach space
Schauder basis
Decay rate
MATEMATICA APLICADA
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spelling On decay rates of the solutions of parabolic Cauchy problemsBonet Solves, José Antonio|||0000-0002-9096-6380Lusky, WolfgangTaskinen, JariParabolic PDECauchy problemBanach spaceSchauder basisDecay rateMATEMATICA APLICADA[EN] We consider the Cauchy problem for a general class of parabolic partial differential equations in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast growing weight w, there is a Schauder basis (e(n))(n=1)(infinity) in L-w(p)(R-N) with the following property: given an arbitrary positive integer m there exists n(m) > 0 such that, if the initial data f belongs to the closed linear span of e(n) with n >= n(m), then the decay rate of the solution of the problem is at least t(-m) for large times t. The result generalizes the recent study of the authors concerning the classical linear heat equation. We present variants of the result having different methods of proofs and also consider finite polynomial decay rates instead of unlimited m.The research of Bonet was partially supported by the projects MTM2016-76647P and GV Prometeo/2017/102 (Spain). The research of Taskinen was partially supported by a research grant from the Faculty of Science of the University of Helsinki.Cambridge University PressDepartamento de Matemática AplicadaEscuela Técnica Superior de ArquitecturaInstituto Universitario de Matemática Pura y AplicadaGENERALITAT VALENCIANAAGENCIA ESTATAL DE INVESTIGACIONRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-06-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/189475reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIAGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES.open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1894752026-06-13T07:49:27Z
dc.title.none.fl_str_mv On decay rates of the solutions of parabolic Cauchy problems
title On decay rates of the solutions of parabolic Cauchy problems
spellingShingle On decay rates of the solutions of parabolic Cauchy problems
Bonet Solves, José Antonio|||0000-0002-9096-6380
Parabolic PDE
Cauchy problem
Banach space
Schauder basis
Decay rate
MATEMATICA APLICADA
title_short On decay rates of the solutions of parabolic Cauchy problems
title_full On decay rates of the solutions of parabolic Cauchy problems
title_fullStr On decay rates of the solutions of parabolic Cauchy problems
title_full_unstemmed On decay rates of the solutions of parabolic Cauchy problems
title_sort On decay rates of the solutions of parabolic Cauchy problems
dc.creator.none.fl_str_mv Bonet Solves, José Antonio|||0000-0002-9096-6380
Lusky, Wolfgang
Taskinen, Jari
author Bonet Solves, José Antonio|||0000-0002-9096-6380
author_facet Bonet Solves, José Antonio|||0000-0002-9096-6380
Lusky, Wolfgang
Taskinen, Jari
author_role author
author2 Lusky, Wolfgang
Taskinen, Jari
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Arquitectura
Instituto Universitario de Matemática Pura y Aplicada
GENERALITAT VALENCIANA
AGENCIA ESTATAL DE INVESTIGACION
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Parabolic PDE
Cauchy problem
Banach space
Schauder basis
Decay rate
MATEMATICA APLICADA
topic Parabolic PDE
Cauchy problem
Banach space
Schauder basis
Decay rate
MATEMATICA APLICADA
description [EN] We consider the Cauchy problem for a general class of parabolic partial differential equations in the Euclidean space R-N. We show that given a weighted L-p-space L-w(p)(R-N) with 1 <= p < infinity and a fast growing weight w, there is a Schauder basis (e(n))(n=1)(infinity) in L-w(p)(R-N) with the following property: given an arbitrary positive integer m there exists n(m) > 0 such that, if the initial data f belongs to the closed linear span of e(n) with n >= n(m), then the decay rate of the solution of the problem is at least t(-m) for large times t. The result generalizes the recent study of the authors concerning the classical linear heat equation. We present variants of the result having different methods of proofs and also consider finite polynomial decay rates instead of unlimited m.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-06-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/189475
url https://riunet.upv.es/handle/10251/189475
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 MTM2016-76647-P ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y ANALISIS TIEMPO-FRECUENCIA
Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F102 ANALISIS FUNCIONAL, TEORIA DE OPERADORES Y APLICACIONES.
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
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
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Cambridge University Press
publisher.none.fl_str_mv Cambridge University Press
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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