Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case

Autores
Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections.
Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; Chile
Fil: Quirós, Fernando. Universidad Autonoma de Madrid; España
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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
Porous medium equation
Asymptotic behavior,
Exterior domain
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:11336/89716
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/89716
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional caseCortázar, CarmenQuirós, FernandoWolanski, Noemi IrenePorous medium equationAsymptotic behavior,Exterior domainMatched asymptoticshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections.Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; ChileFil: Quirós, Fernando. Universidad Autonoma de Madrid; EspañaFil: 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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaSociety for Industrial and Applied Mathematics2018-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/89716Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene; Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 50; 3; 9-2018; 2664-26800036-1410CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1610.04772.pdfinfo:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/16M110191Xinfo:eu-repo/semantics/altIdentifier/doi/10.1137/16M110191Xinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:09:43Zoai:ri.conicet.gov.ar:11336/89716instacron: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:34982025-10-22 12:09:44.228CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
title Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
spellingShingle Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
Cortázar, Carmen
Porous medium equation
Asymptotic behavior,
Exterior domain
Matched asymptotics
title_short Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
title_full Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
title_fullStr Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
title_full_unstemmed Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
title_sort Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case
dc.creator.none.fl_str_mv Cortázar, Carmen
Quirós, Fernando
Wolanski, Noemi Irene
author Cortázar, Carmen
author_facet Cortázar, Carmen
Quirós, Fernando
Wolanski, Noemi Irene
author_role author
author2 Quirós, Fernando
Wolanski, Noemi Irene
author2_role author
author
dc.subject.none.fl_str_mv Porous medium equation
Asymptotic behavior,
Exterior domain
Matched asymptotics
topic Porous medium equation
Asymptotic behavior,
Exterior domain
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 consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections.
Fil: Cortázar, Carmen. Pontificia Universidad Católica de Chile; Chile
Fil: Quirós, Fernando. Universidad Autonoma de Madrid; España
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". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We consider the porous medium equation in an exterior two-dimensional domain that excludes a hole, with zero Dirichlet data on its boundary. Gilding and Goncerzewicz proved in 2007 that in the far-field scale, which is the adequate one to describe the movement of the free boundary, solutions to this problem with integrable and compactly supported initial data behave as an instantaneous point-source solution for the equation with a variable mass that decays to 0 in a precise way, determined by the initial data and the hole. In this paper, starting from their result in the far field, we study the large time behavior in the near field, in scales that evolve more slowly than the free boundary. In this way we get, in particular, the final profile and decay rate on compact sets. Spatial dimension two is critical for this problem, and involves logarithmic corrections.
publishDate 2018
dc.date.none.fl_str_mv 2018-09
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/11336/89716
Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene; Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 50; 3; 9-2018; 2664-2680
0036-1410
CONICET Digital
CONICET
url http://hdl.handle.net/11336/89716
identifier_str_mv Cortázar, Carmen; Quirós, Fernando; Wolanski, Noemi Irene; Near-field asymptotics for the porous medium equation in exterior domains: The critical two-dimensional case; Society for Industrial and Applied Mathematics; Siam Journal On Mathematical Analysis; 50; 3; 9-2018; 2664-2680
0036-1410
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/pdf/1610.04772.pdf
info:eu-repo/semantics/altIdentifier/url/https://epubs.siam.org/doi/10.1137/16M110191X
info:eu-repo/semantics/altIdentifier/doi/10.1137/16M110191X
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 Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
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 12.982451

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