Asymptotic Behavior for a nonlocal diffusion equation on the half line

Autores
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the large time behavior of solutions to a nonlocal diffusion equation, ut=J∗u−u with J smooth, radially symmetric and compactly supported, posed in R+ with zero Dirichlet boundary conditions. In the far-field scale, ξ1≤xt−1/2≤ξ2 with ξ1,ξ2>0, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, hence tu(x,t) is bounded above and below by positive constants in this region for large times. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. In compact sets, after scaling the solution by a factor t3/2, it converges to a multiple of the unique stationary solution of the problem that behaves as x at infinity. The precise proportionality factor is obtained through a matching procedure with the far-field limit. Finally, in the very far-field, x≥t1/2g(t) with g(t)→∞, the solution is proved to be of order o(t−1).
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. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Nonlocal Diffusion
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:11336/18995
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Asymptotic Behavior for a nonlocal diffusion equation on the half lineCortázar, CarmenElgueta, ManuelQuirós, FernandoWolanski, Noemi IreneNonlocal DiffusionAsymptotic BehaviorMatched Asymptoticshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the large time behavior of solutions to a nonlocal diffusion equation, ut=J∗u−u with J smooth, radially symmetric and compactly supported, posed in R+ with zero Dirichlet boundary conditions. In the far-field scale, ξ1≤xt−1/2≤ξ2 with ξ1,ξ2>0, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, hence tu(x,t) is bounded above and below by positive constants in this region for large times. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. In compact sets, after scaling the solution by a factor t3/2, it converges to a multiple of the unique stationary solution of the problem that behaves as x at infinity. The precise proportionality factor is obtained through a matching procedure with the far-field limit. Finally, in the very far-field, x≥t1/2g(t) with g(t)→∞, the solution is proved to be of order o(t−1).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. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaAmer Inst Mathematical Sciences2015-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/zipapplication/pdfhttp://hdl.handle.net/11336/18995Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a nonlocal diffusion equation on the half line; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 35; 4; 4-2015; 1391-14071078-0947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2015.35.1391info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10559info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1308.4897info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:59:52Zoai:ri.conicet.gov.ar:11336/18995instacron: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 09:59:53.215CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic Behavior for a nonlocal diffusion equation on the half line
title Asymptotic Behavior for a nonlocal diffusion equation on the half line
spellingShingle Asymptotic Behavior for a nonlocal diffusion equation on the half line
Cortázar, Carmen
Nonlocal Diffusion
Asymptotic Behavior
Matched Asymptotics
title_short Asymptotic Behavior for a nonlocal diffusion equation on the half line
title_full Asymptotic Behavior for a nonlocal diffusion equation on the half line
title_fullStr Asymptotic Behavior for a nonlocal diffusion equation on the half line
title_full_unstemmed Asymptotic Behavior for a nonlocal diffusion equation on the half line
title_sort Asymptotic Behavior for a nonlocal diffusion equation on the half line
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
Asymptotic Behavior
Matched Asymptotics
topic Nonlocal Diffusion
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 We study the large time behavior of solutions to a nonlocal diffusion equation, ut=J∗u−u with J smooth, radially symmetric and compactly supported, posed in R+ with zero Dirichlet boundary conditions. In the far-field scale, ξ1≤xt−1/2≤ξ2 with ξ1,ξ2>0, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, hence tu(x,t) is bounded above and below by positive constants in this region for large times. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. In compact sets, after scaling the solution by a factor t3/2, it converges to a multiple of the unique stationary solution of the problem that behaves as x at infinity. The precise proportionality factor is obtained through a matching procedure with the far-field limit. Finally, in the very far-field, x≥t1/2g(t) with g(t)→∞, the solution is proved to be of order o(t−1).
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. Universidad Autónoma de Madrid; España. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We study the large time behavior of solutions to a nonlocal diffusion equation, ut=J∗u−u with J smooth, radially symmetric and compactly supported, posed in R+ with zero Dirichlet boundary conditions. In the far-field scale, ξ1≤xt−1/2≤ξ2 with ξ1,ξ2>0, the asymptotic behavior is given by a multiple of the dipole solution for the local heat equation, hence tu(x,t) is bounded above and below by positive constants in this region for large times. The proportionality constant is determined from a conservation law, related to the asymptotic first momentum. In compact sets, after scaling the solution by a factor t3/2, it converges to a multiple of the unique stationary solution of the problem that behaves as x at infinity. The precise proportionality factor is obtained through a matching procedure with the far-field limit. Finally, in the very far-field, x≥t1/2g(t) with g(t)→∞, the solution is proved to be of order o(t−1).
publishDate 2015
dc.date.none.fl_str_mv 2015-04
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/11336/18995
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a nonlocal diffusion equation on the half line; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 35; 4; 4-2015; 1391-1407
1078-0947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18995
identifier_str_mv Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic Behavior for a nonlocal diffusion equation on the half line; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 35; 4; 4-2015; 1391-1407
1078-0947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2015.35.1391
info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=10559
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1308.4897
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/zip
application/pdf
dc.publisher.none.fl_str_mv Amer Inst Mathematical Sciences
publisher.none.fl_str_mv Amer Inst Mathematical Sciences
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 13.13397

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