The Galerkin–Fourier method for the study of nonlocal parabolic equations

The aim of this paper is the study of a type of nonlocal parabolic equation. The formulation includes a convolution kernel k in the diffusion term and a design function h that plays the role of the diffusion coefficient. The main goal is twofold: On the one hand, the existence and uniqueness of nonl...

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Detalhes bibliográficos
Autores: Andrés Abellán, María Fuensanta, Muñoz Martín, Julio
Tipo de documento: artigo
Data de publicação:2019
País:España
Recursos:Universidad de Castilla-La Mancha
Repositório:RUIdeRA. Repositorio Institucional de la UCLM
OAI Identifier:oai:ruidera.uclm.es:10578/28979
Acesso em linha:http://hdl.handle.net/10578/28979
Access Level:Acceso aberto
Palavra-chave:Approximation of partial differential equations
Nonlocal parabolic equations
Optimal control
Integral equations
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spelling The Galerkin–Fourier method for the study of nonlocal parabolic equationsAndrés Abellán, María FuensantaMuñoz Martín, JulioApproximation of partial differential equationsNonlocal parabolic equationsOptimal controlIntegral equationsThe aim of this paper is the study of a type of nonlocal parabolic equation. The formulation includes a convolution kernel k in the diffusion term and a design function h that plays the role of the diffusion coefficient. The main goal is twofold: On the one hand, the existence and uniqueness of nonlocal solution are deduced. Also, a comprehensive and rigorous procedure, which is based on the classical Galerkin–Fourier Method, is performed. As in the classical setting, the appropriate choice of the Gelfand triplet will guarantee the differentiation and therefore the operational technique for the study of the parabolic equation. On the other hand, the convergence of the nonlocal solution as the kernel k converges to a Dirac Delta is studied. The series expansion of the nonlocal solution allows us, in an easy way, to show its convergence to the solution of the corresponding local parabolic equation.Springer Nature Switzerland AG202120212019info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttp://hdl.handle.net/10578/28979reponame:RUIdeRA. Repositorio Institucional de la UCLMinstname:Universidad de Castilla-La ManchaInglésinfo:eu-repo/semantics/openAccessoai:ruidera.uclm.es:10578/289792026-05-27T07:36:41Z
dc.title.none.fl_str_mv The Galerkin–Fourier method for the study of nonlocal parabolic equations
title The Galerkin–Fourier method for the study of nonlocal parabolic equations
spellingShingle The Galerkin–Fourier method for the study of nonlocal parabolic equations
Andrés Abellán, María Fuensanta
Approximation of partial differential equations
Nonlocal parabolic equations
Optimal control
Integral equations
title_short The Galerkin–Fourier method for the study of nonlocal parabolic equations
title_full The Galerkin–Fourier method for the study of nonlocal parabolic equations
title_fullStr The Galerkin–Fourier method for the study of nonlocal parabolic equations
title_full_unstemmed The Galerkin–Fourier method for the study of nonlocal parabolic equations
title_sort The Galerkin–Fourier method for the study of nonlocal parabolic equations
dc.creator.none.fl_str_mv Andrés Abellán, María Fuensanta
Muñoz Martín, Julio
author Andrés Abellán, María Fuensanta
author_facet Andrés Abellán, María Fuensanta
Muñoz Martín, Julio
author_role author
author2 Muñoz Martín, Julio
author2_role author
dc.subject.none.fl_str_mv Approximation of partial differential equations
Nonlocal parabolic equations
Optimal control
Integral equations
topic Approximation of partial differential equations
Nonlocal parabolic equations
Optimal control
Integral equations
description The aim of this paper is the study of a type of nonlocal parabolic equation. The formulation includes a convolution kernel k in the diffusion term and a design function h that plays the role of the diffusion coefficient. The main goal is twofold: On the one hand, the existence and uniqueness of nonlocal solution are deduced. Also, a comprehensive and rigorous procedure, which is based on the classical Galerkin–Fourier Method, is performed. As in the classical setting, the appropriate choice of the Gelfand triplet will guarantee the differentiation and therefore the operational technique for the study of the parabolic equation. On the other hand, the convergence of the nonlocal solution as the kernel k converges to a Dirac Delta is studied. The series expansion of the nonlocal solution allows us, in an easy way, to show its convergence to the solution of the corresponding local parabolic equation.
publishDate 2019
dc.date.none.fl_str_mv 2019
2021
2021
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10578/28979
url http://hdl.handle.net/10578/28979
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
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 Springer Nature Switzerland AG
publisher.none.fl_str_mv Springer Nature Switzerland AG
dc.source.none.fl_str_mv reponame:RUIdeRA. Repositorio Institucional de la UCLM
instname:Universidad de Castilla-La Mancha
instname_str Universidad de Castilla-La Mancha
reponame_str RUIdeRA. Repositorio Institucional de la UCLM
collection RUIdeRA. Repositorio Institucional de la UCLM
repository.name.fl_str_mv
repository.mail.fl_str_mv
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