Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains

Autores
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the long time behavior of solutions to the nonlocal diffusion equation ∂tu = J ∗ u − u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ξ1 ≤ |x|t −1/2 ≤ ξ2, ξ1, ξ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R−: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t 1/2h(t), limt→∞ h(t) = 0, the solution scaled by a factor t 3/2 /(|x| + 1) converges to a stationary solution of the problem that behaves as b ±x as x → ±∞. The constants b ± are obtained through a matching procedure with the far field limit. In the very far field, |x|≥t 1/2 g(t), g(t) → ∞, the solution has 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. 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
Difusión no local
Comportamiento asintótico
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:11336/18936
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domainsCortázar, CarmenElgueta, ManuelQuirós, FernandoWolanski, Noemi IreneDifusión no localComportamiento asintóticohttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the long time behavior of solutions to the nonlocal diffusion equation ∂tu = J ∗ u − u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ξ1 ≤ |x|t −1/2 ≤ ξ2, ξ1, ξ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R−: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t 1/2h(t), limt→∞ h(t) = 0, the solution scaled by a factor t 3/2 /(|x| + 1) converges to a stationary solution of the problem that behaves as b ±x as x → ±∞. The constants b ± are obtained through a matching procedure with the far field limit. In the very far field, |x|≥t 1/2 g(t), g(t) → ∞, the solution has 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. 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"; ArgentinaSiam Publications2016-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18936Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains; Siam Publications; Siam Journal On Mathematical Analysis; 48; 3; 3-2016; 1549-15740036-14101095-7154CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1137/151006287info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/151006287info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1412.0731info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:28:39Zoai:ri.conicet.gov.ar:11336/18936instacron: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:34982025-09-29 10:28:39.604CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
spellingShingle Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
Cortázar, Carmen
Difusión no local
Comportamiento asintótico
title_short Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_full Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_fullStr Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_full_unstemmed Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
title_sort Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains
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 Difusión no local
Comportamiento asintótico
topic Difusión no local
Comportamiento asintótico
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 long time behavior of solutions to the nonlocal diffusion equation ∂tu = J ∗ u − u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ξ1 ≤ |x|t −1/2 ≤ ξ2, ξ1, ξ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R−: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t 1/2h(t), limt→∞ h(t) = 0, the solution scaled by a factor t 3/2 /(|x| + 1) converges to a stationary solution of the problem that behaves as b ±x as x → ±∞. The constants b ± are obtained through a matching procedure with the far field limit. In the very far field, |x|≥t 1/2 g(t), g(t) → ∞, the solution has 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. 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 We study the long time behavior of solutions to the nonlocal diffusion equation ∂tu = J ∗ u − u in an exterior one-dimensional domain, with zero Dirichlet data on the complement. In the far field scale, ξ1 ≤ |x|t −1/2 ≤ ξ2, ξ1, ξ2 > 0, this behavior is given by a multiple of the dipole solution for the local heat equation with a diffusivity determined by J. However, the proportionality constant is not the same on R+ and R−: it is given by the asymptotic first moment of the solution on the corresponding half line, which can be computed in terms of the initial data. In the near field scale, |x| ≤ t 1/2h(t), limt→∞ h(t) = 0, the solution scaled by a factor t 3/2 /(|x| + 1) converges to a stationary solution of the problem that behaves as b ±x as x → ±∞. The constants b ± are obtained through a matching procedure with the far field limit. In the very far field, |x|≥t 1/2 g(t), g(t) → ∞, the solution has order o(t −1 ).
publishDate 2016
dc.date.none.fl_str_mv 2016-03
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/11336/18936
Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains; Siam Publications; Siam Journal On Mathematical Analysis; 48; 3; 3-2016; 1549-1574
0036-1410
1095-7154
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18936
identifier_str_mv Cortázar, Carmen; Elgueta, Manuel; Quirós, Fernando; Wolanski, Noemi Irene; Asymptotic behavior for a one-dimensional nonlocal diffusion equation in exterior domains; Siam Publications; Siam Journal On Mathematical Analysis; 48; 3; 3-2016; 1549-1574
0036-1410
1095-7154
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1137/151006287
info:eu-repo/semantics/altIdentifier/url/http://epubs.siam.org/doi/abs/10.1137/151006287
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1412.0731
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
dc.publisher.none.fl_str_mv Siam Publications
publisher.none.fl_str_mv Siam Publications
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 13.070432

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