Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes

Autores
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, ut = J ∗u −u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on RN \Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.
Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; Chile
Fil: Elgueta, Manuel. Pontificia Universidad Católica de Chile; Chile
Fil: Quirós, Fernando. Universidad Autónoma de Madrid; España
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Nonlocal Diffusion
Exterior Domain
Asymptotic Behavior
Matched Asymptotics
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/19929
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/19929
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with HolesCortázar, CarmenElgueta, ManuelQuirós, FernandoWolanski, Noemi IreneNonlocal DiffusionExterior DomainAsymptotic BehaviorMatched Asymptoticshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, ut = J ∗u −u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on RN \Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; ChileFil: Elgueta, Manuel. Pontificia Universidad Católica de Chile; ChileFil: Quirós, Fernando. Universidad Autónoma de Madrid; EspañaFil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSpringer2012-08info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19929Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes; Springer; Archive For Rational Mechanics And Analysis; 205; 2; 8-2012; 673-6970003-95271432-0673CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-012-0519-2info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00205-012-0519-2info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.1761info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:47:22Zoai:ri.conicet.gov.ar:11336/19929instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:47:23.098CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
spellingShingle Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
Cortázar, Carmen
Nonlocal Diffusion
Exterior Domain
Asymptotic Behavior
Matched Asymptotics
title_short Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_full Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_fullStr Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_full_unstemmed Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
title_sort Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes
dc.creator.none.fl_str_mv Cortázar, Carmen
Elgueta, Manuel
Quirós, Fernando
Wolanski, Noemi Irene
author Cortázar, Carmen
author_facet Cortázar, Carmen
Elgueta, Manuel
Quirós, Fernando
Wolanski, Noemi Irene
author_role author
author2 Elgueta, Manuel
Quirós, Fernando
Wolanski, Noemi Irene
author2_role author
author
author
dc.subject.none.fl_str_mv Nonlocal Diffusion
Exterior Domain
Asymptotic Behavior
Matched Asymptotics
topic Nonlocal Diffusion
Exterior Domain
Asymptotic Behavior
Matched Asymptotics
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, ut = J ∗u −u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on RN \Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.
Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; Chile
Fil: Elgueta, Manuel. Pontificia Universidad Católica de Chile; Chile
Fil: Quirós, Fernando. Universidad Autónoma de Madrid; España
Fil: Wolanski, Noemi Irene. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description The paper deals with the asymptotic behavior of solutions to a non-local diffusion equation, ut = J ∗u −u := Lu, in an exterior domain, Ω, which excludes one or several holes, and with zero Dirichlet data on RN \Ω. When the space dimension is three or more this behavior is given by a multiple of the fundamental solution of the heat equation away from the holes. On the other hand, if the solution is scaled according to its decay factor, close to the holes it behaves like a function that is L-harmonic, Lu = 0, in the exterior domain and vanishes in its complement. The height of such a function at infinity is determined through a matching procedure with the multiple of the fundamental solution of the heat equation representing the outer behavior. The inner and the outer behaviors can be presented in a unified way through a suitable global approximation.
publishDate 2012
dc.date.none.fl_str_mv 2012-08
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/19929
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes; Springer; Archive For Rational Mechanics And Analysis; 205; 2; 8-2012; 673-697
0003-9527
1432-0673
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19929
identifier_str_mv Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a Nonlocal Diffusion Equation in Domains with Holes; Springer; Archive For Rational Mechanics And Analysis; 205; 2; 8-2012; 673-697
0003-9527
1432-0673
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-012-0519-2
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00205-012-0519-2
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1111.1761
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.885934

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