Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case

In this paper we continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption ut=Lu−upin RN×(0,∞),u(x,0)=u0(x)in RN, where p>1, u0⩾0 and bounded and Lu(x,t)=∫J(x−y)(u(y,t)−u(x,t))dy with J∈C0∞(Bd), radially symmetric, J>0 in Bd, with...

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Autores: Salort, Ariel Martin, Afonso Mourao Terra, Joana Isabel, Wolanski, Noemi Irene
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2015
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/116926
Acesso em linha:http://hdl.handle.net/11336/116926
Access Level:Acceso aberto
Palavra-chave:LARGE TIME BEHAVIOR
NONLOCAL DIFFUSION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical caseSalort, Ariel MartinAfonso Mourao Terra, Joana IsabelWolanski, Noemi IreneLARGE TIME BEHAVIORNONLOCAL DIFFUSIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper we continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption ut=Lu−upin RN×(0,∞),u(x,0)=u0(x)in RN, where p>1, u0⩾0 and bounded and Lu(x,t)=∫J(x−y)(u(y,t)−u(x,t))dy with J∈C0∞(Bd), radially symmetric, J>0 in Bd, with ∫J=1. Our assumption on the initial datum is that 0⩽u0∈L∞(RN) and |x|αu0(x)→A>0as |x|→∞. This problem was studied in [Proc. Amer. Math. Soc. 139(4) (2011), 1421–1432; Discrete Cont. Dyn. Syst. A, 31(2) (2011), 581–605] in the supercritical and critical cases p⩾1+2/α. In the present paper we study the subcritical case 10. Of independent interest is our study of the positive eigenfunction of the operator L in the ball BR in the L∞ setting that we include in Section 3.Fil: Salort, Ariel Martin. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Afonso Mourao Terra, Joana Isabel. 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; 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"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaIOS Press2015-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/116926Salort, Ariel Martin; Afonso Mourao Terra, Joana Isabel; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case; IOS Press; Asymptotic Analysis; 95; 1-2; 10-2015; 39-570921-7134CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://content.iospress.com/articles/asymptotic-analysis/asy1320info:eu-repo/semantics/altIdentifier/doi/10.3233/ASY-151320info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:37:42Zoai:ri.conicet.gov.ar:11336/116926instacron: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:34982024-05-08 13:37:43.256CONICET 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: The subcritical case
title Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
spellingShingle Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
Salort, Ariel Martin
LARGE TIME BEHAVIOR
NONLOCAL DIFFUSION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
title_full Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
title_fullStr Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
title_full_unstemmed Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
title_sort Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case
dc.creator.none.fl_str_mv Salort, Ariel Martin
Afonso Mourao Terra, Joana Isabel
Wolanski, Noemi Irene
author Salort, Ariel Martin
author_facet Salort, Ariel Martin
Afonso Mourao Terra, Joana Isabel
Wolanski, Noemi Irene
author_role author
author2 Afonso Mourao Terra, Joana Isabel
Wolanski, Noemi Irene
author2_role author
author
dc.subject.none.fl_str_mv LARGE TIME BEHAVIOR
NONLOCAL DIFFUSION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic LARGE TIME BEHAVIOR
NONLOCAL DIFFUSION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description In this paper we continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption ut=Lu−upin RN×(0,∞),u(x,0)=u0(x)in RN, where p>1, u0⩾0 and bounded and Lu(x,t)=∫J(x−y)(u(y,t)−u(x,t))dy with J∈C0∞(Bd), radially symmetric, J>0 in Bd, with ∫J=1. Our assumption on the initial datum is that 0⩽u0∈L∞(RN) and |x|αu0(x)→A>0as |x|→∞. This problem was studied in [Proc. Amer. Math. Soc. 139(4) (2011), 1421–1432; Discrete Cont. Dyn. Syst. A, 31(2) (2011), 581–605] in the supercritical and critical cases p⩾1+2/α. In the present paper we study the subcritical case 10. Of independent interest is our study of the positive eigenfunction of the operator L in the ball BR in the L∞ setting that we include in Section 3.
publishDate 2015
dc.date.none.fl_str_mv 2015-10
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/11336/116926
Salort, Ariel Martin; Afonso Mourao Terra, Joana Isabel; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case; IOS Press; Asymptotic Analysis; 95; 1-2; 10-2015; 39-57
0921-7134
CONICET Digital
CONICET
url http://hdl.handle.net/11336/116926
identifier_str_mv Salort, Ariel Martin; Afonso Mourao Terra, Joana Isabel; Wolanski, Noemi Irene; Large time behavior for a nonlocal diffusion equation with absorption and bounded initial data: The subcritical case; IOS Press; Asymptotic Analysis; 95; 1-2; 10-2015; 39-57
0921-7134
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://content.iospress.com/articles/asymptotic-analysis/asy1320
info:eu-repo/semantics/altIdentifier/doi/10.3233/ASY-151320
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
application/pdf
dc.publisher.none.fl_str_mv IOS Press
publisher.none.fl_str_mv IOS Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,81155

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