Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data

Autores
Terra, Joana; Wolanski, Noemi Irene
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the large time behavior of nonnegative solutions of the Cauchy problem u t = R J ( x − y )( u ( y,t ) − u ( x,t )) dy − u p , u ( x, 0) = u 0 ( x ) ∈ L ∞ , where | x | α u 0 ( x ) → A > 0 as | x |→∞ . One of our main goals is the study of the critical case p = 1 + 2 /α for 0 < α < N , left open in previous articles, for which we prove that t α/ 2 | u ( x,t ) − U ( x,t ) | → 0 where U is the solution of the heat equation with absorption with initial datum U ( x, 0) = C A,N | x | − α . Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u 0 in the supercritical case and also in the critical case ( p = 1 + 2 /N ) for bounded and integrable u 0 .
Fil: Terra, Joana. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Nonlocal diffusion
Large time behavior
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:11336/14924
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Large time behavior for a nonlocal diffusion equation with absorption and bounded initial dataTerra, JoanaWolanski, Noemi IreneNonlocal diffusionLarge time behaviorhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the large time behavior of nonnegative solutions of the Cauchy problem u t = R J ( x − y )( u ( y,t ) − u ( x,t )) dy − u p , u ( x, 0) = u 0 ( x ) ∈ L ∞ , where | x | α u 0 ( x ) → A > 0 as | x |→∞ . One of our main goals is the study of the critical case p = 1 + 2 /α for 0 < α < N , left open in previous articles, for which we prove that t α/ 2 | u ( x,t ) − U ( x,t ) | → 0 where U is the solution of the heat equation with absorption with initial datum U ( x, 0) = C A,N | x | − α . Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u 0 in the supercritical case and also in the critical case ( p = 1 + 2 /N ) for bounded and integrable u 0 .Fil: Terra, Joana. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaAmer Inst Mathematical Sciences2011-10info: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/11336/14924Terra, Joana; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 31; 2; 10-2011; 581-6051078-0947enginfo:eu-repo/semantics/altIdentifier/url/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6304info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2011.31.581info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:07:19Zoai:ri.conicet.gov.ar:11336/14924instacron: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:34982025-09-10 13:07:19.244CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
title Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
spellingShingle Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
Terra, Joana
Nonlocal diffusion
Large time behavior
title_short Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
title_full Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
title_fullStr Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
title_full_unstemmed Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data
title_sort Large time behavior for a nonlocal diffusion equation with absorption and bounded 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 Nonlocal diffusion
Large time behavior
topic Nonlocal diffusion
Large time behavior
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 nonnegative solutions of the Cauchy problem u t = R J ( x − y )( u ( y,t ) − u ( x,t )) dy − u p , u ( x, 0) = u 0 ( x ) ∈ L ∞ , where | x | α u 0 ( x ) → A > 0 as | x |→∞ . One of our main goals is the study of the critical case p = 1 + 2 /α for 0 < α < N , left open in previous articles, for which we prove that t α/ 2 | u ( x,t ) − U ( x,t ) | → 0 where U is the solution of the heat equation with absorption with initial datum U ( x, 0) = C A,N | x | − α . Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u 0 in the supercritical case and also in the critical case ( p = 1 + 2 /N ) for bounded and integrable u 0 .
Fil: Terra, Joana. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Wolanski, Noemi Irene. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We study the large time behavior of nonnegative solutions of the Cauchy problem u t = R J ( x − y )( u ( y,t ) − u ( x,t )) dy − u p , u ( x, 0) = u 0 ( x ) ∈ L ∞ , where | x | α u 0 ( x ) → A > 0 as | x |→∞ . One of our main goals is the study of the critical case p = 1 + 2 /α for 0 < α < N , left open in previous articles, for which we prove that t α/ 2 | u ( x,t ) − U ( x,t ) | → 0 where U is the solution of the heat equation with absorption with initial datum U ( x, 0) = C A,N | x | − α . Our proof, involving sequences of rescalings of the solution, allows us to establish also the large time behavior of solutions having more general nonintegrable initial data u 0 in the supercritical case and also in the critical case ( p = 1 + 2 /N ) for bounded and integrable u 0 .
publishDate 2011
dc.date.none.fl_str_mv 2011-10
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/11336/14924
Terra, Joana; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 31; 2; 10-2011; 581-605
1078-0947
url http://hdl.handle.net/11336/14924
identifier_str_mv Terra, Joana; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data; Amer Inst Mathematical Sciences; Discrete And Continuous Dynamical Systems; 31; 2; 10-2011; 581-605
1078-0947
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://aimsciences.org/journals/displayArticlesnew.jsp?paperID=6304
info:eu-repo/semantics/altIdentifier/doi/10.3934/dcds.2011.31.581
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 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 12.993085

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