Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data

Autores
Terra, Joana; Wolanski, Noemi Irene
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum.
Fil: Terra, Joana. Universidad de Buenos Aires; Argentina
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
BOUNDARY VALUE PROBLEMS
NONLOCAL DIFFUSION
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:11336/125434
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial dataTerra, JoanaWolanski, Noemi IreneBOUNDARY VALUE PROBLEMSNONLOCAL DIFFUSIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum.Fil: Terra, Joana. Universidad de Buenos Aires; ArgentinaFil: 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"; ArgentinaAmerican Mathematical Society2011-04info: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/11336/125434Terra, Joana; Wolanski, Noemi Irene; Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data; American Mathematical Society; Proceedings of the American Mathematical Society; 139; 4; 4-2011; 1421-14320002-9939CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2010-10612-3info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2011-139-04/S0002-9939-2010-10612-3/home.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:01:16Zoai:ri.conicet.gov.ar:11336/125434instacron: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 10:01:16.877CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
title Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
spellingShingle Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
Terra, Joana
BOUNDARY VALUE PROBLEMS
NONLOCAL DIFFUSION
title_short Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
title_full Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
title_fullStr Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
title_full_unstemmed Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
title_sort Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data
dc.creator.none.fl_str_mv Terra, Joana
Wolanski, Noemi Irene
author Terra, Joana
author_facet Terra, Joana
Wolanski, Noemi Irene
author_role author
author2 Wolanski, Noemi Irene
author2_role author
dc.subject.none.fl_str_mv BOUNDARY VALUE PROBLEMS
NONLOCAL DIFFUSION
topic BOUNDARY VALUE PROBLEMS
NONLOCAL DIFFUSION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum.
Fil: Terra, Joana. Universidad de Buenos Aires; Argentina
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 In this paper we study the asymptotic behavior as time goes to infinity of the solution to a nonlocal diffusion equation with absorption modeled by a powerlike reaction -up, p > 1 and set in ℝN. We consider a bounded, nonnegative initial datum u0 that behaves like a negative power at infinity. That is, |x|αu0(x) → A > 0 as |x| → ∞ with 0 < α ≤ N. We prove that, in the supercritical case p > 1+2/α, the solution behaves asymptotically as that of the heat equation (with diffusivity a related to the nonlocal operator) with the same initial datum.
publishDate 2011
dc.date.none.fl_str_mv 2011-04
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/11336/125434
Terra, Joana; Wolanski, Noemi Irene; Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data; American Mathematical Society; Proceedings of the American Mathematical Society; 139; 4; 4-2011; 1421-1432
0002-9939
CONICET Digital
CONICET
url http://hdl.handle.net/11336/125434
identifier_str_mv Terra, Joana; Wolanski, Noemi Irene; Asymptotic behavior for a nonlocal diffusion equation with absorption and nonintegrable initial data; American Mathematical Society; Proceedings of the American Mathematical Society; 139; 4; 4-2011; 1421-1432
0002-9939
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-2010-10612-3
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2011-139-04/S0002-9939-2010-10612-3/home.html
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 American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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
_version_ 1842269686997188608
score 13.13397

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