A two phase elliptic singular perturbation problem with a forcing term

Autores
Lederman, Claudia Beatriz; Wolanski, Noemi Irene
Año de publicación
2006
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the following two phase elliptic singular perturbation problem: Due=be(ue)+fe in WÌRN, where e>0, be(s)=(1/e)b(s/e), with b a Lipschitz function satisfying b>0 in (0,1), bº0 outside (0,1) and òb(s)ds = M . The functions ue and fe are uniformly bounded. One of the motivations for the study of this problem is that it appears in the analysis of the propagation of flames in the high activation energy limit, when sources are present. We obtain uniform estimates, we pass to the limit (e®0) and we show that limit functions are solutions to the two phase free boundary problem Du = f x{mº0}      in    W ¶{u>0},                                                                               |Ñu+|2 - |Ñu-|2 = 2M       on    WǶ{u>0}, where f = limfe , in a viscosity sense and in a pointwise sense at regular free boundary points. In addition, we show that the free boundary is smooth and thus limit functions are classical solutions to the free boundary problem, under suitable assumptions. Some of the results obtained are new even in the case feº0. The results in this paper also apply to other combustion models. For instance, models with nonlocal diffusion and/or transport. Several of these applications are discussed here and we get, in some cases, the full regularity of the free boundary.
Fil: Lederman, Claudia Beatriz. 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; 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Materia
FREE BOUNDARY PROBLEM
TWO PHASE
VISCOSITY SOLUTIONS
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:11336/276544
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling A two phase elliptic singular perturbation problem with a forcing termLederman, Claudia BeatrizWolanski, Noemi IreneFREE BOUNDARY PROBLEMTWO PHASEVISCOSITY SOLUTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the following two phase elliptic singular perturbation problem: Due=be(ue)+fe in WÌRN, where e>0, be(s)=(1/e)b(s/e), with b a Lipschitz function satisfying b>0 in (0,1), bº0 outside (0,1) and òb(s)ds = M . The functions ue and fe are uniformly bounded. One of the motivations for the study of this problem is that it appears in the analysis of the propagation of flames in the high activation energy limit, when sources are present. We obtain uniform estimates, we pass to the limit (e®0) and we show that limit functions are solutions to the two phase free boundary problem Du = f x{mº0}      in    W ¶{u>0},                                                                               |Ñu+|2 - |Ñu-|2 = 2M       on    WǶ{u>0}, where f = limfe , in a viscosity sense and in a pointwise sense at regular free boundary points. In addition, we show that the free boundary is smooth and thus limit functions are classical solutions to the free boundary problem, under suitable assumptions. Some of the results obtained are new even in the case feº0. The results in this paper also apply to other combustion models. For instance, models with nonlocal diffusion and/or transport. Several of these applications are discussed here and we get, in some cases, the full regularity of the free boundary.Fil: Lederman, Claudia Beatriz. 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; ArgentinaGauthier-Villars/Editions Elsevier2006-12info: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/11336/276544Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A two phase elliptic singular perturbation problem with a forcing term; Gauthier-Villars/Editions Elsevier; Journal de Mathematiques Pures Et Appliquees; 86; 6; 12-2006; 552-5890021-7824CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0021782406001280info:eu-repo/semantics/altIdentifier/doi/10.1016/j.matpur.2006.10.008info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-12-23T14:20:07Zoai:ri.conicet.gov.ar:11336/276544instacron: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:34982025-12-23 14:20:07.803CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A two phase elliptic singular perturbation problem with a forcing term
title A two phase elliptic singular perturbation problem with a forcing term
spellingShingle A two phase elliptic singular perturbation problem with a forcing term
Lederman, Claudia Beatriz
FREE BOUNDARY PROBLEM
TWO PHASE
VISCOSITY SOLUTIONS
title_short A two phase elliptic singular perturbation problem with a forcing term
title_full A two phase elliptic singular perturbation problem with a forcing term
title_fullStr A two phase elliptic singular perturbation problem with a forcing term
title_full_unstemmed A two phase elliptic singular perturbation problem with a forcing term
title_sort A two phase elliptic singular perturbation problem with a forcing term
dc.creator.none.fl_str_mv Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author Lederman, Claudia Beatriz
author_facet Lederman, Claudia Beatriz
Wolanski, Noemi Irene
author_role author
author2 Wolanski, Noemi Irene
author2_role author
dc.subject.none.fl_str_mv FREE BOUNDARY PROBLEM
TWO PHASE
VISCOSITY SOLUTIONS
topic FREE BOUNDARY PROBLEM
TWO PHASE
VISCOSITY SOLUTIONS
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 following two phase elliptic singular perturbation problem: Due=be(ue)+fe in WÌRN, where e>0, be(s)=(1/e)b(s/e), with b a Lipschitz function satisfying b>0 in (0,1), bº0 outside (0,1) and òb(s)ds = M . The functions ue and fe are uniformly bounded. One of the motivations for the study of this problem is that it appears in the analysis of the propagation of flames in the high activation energy limit, when sources are present. We obtain uniform estimates, we pass to the limit (e®0) and we show that limit functions are solutions to the two phase free boundary problem Du = f x{mº0}      in    W ¶{u>0},                                                                               |Ñu+|2 - |Ñu-|2 = 2M       on    WǶ{u>0}, where f = limfe , in a viscosity sense and in a pointwise sense at regular free boundary points. In addition, we show that the free boundary is smooth and thus limit functions are classical solutions to the free boundary problem, under suitable assumptions. Some of the results obtained are new even in the case feº0. The results in this paper also apply to other combustion models. For instance, models with nonlocal diffusion and/or transport. Several of these applications are discussed here and we get, in some cases, the full regularity of the free boundary.
Fil: Lederman, Claudia Beatriz. 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; 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. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
description We study the following two phase elliptic singular perturbation problem: Due=be(ue)+fe in WÌRN, where e>0, be(s)=(1/e)b(s/e), with b a Lipschitz function satisfying b>0 in (0,1), bº0 outside (0,1) and òb(s)ds = M . The functions ue and fe are uniformly bounded. One of the motivations for the study of this problem is that it appears in the analysis of the propagation of flames in the high activation energy limit, when sources are present. We obtain uniform estimates, we pass to the limit (e®0) and we show that limit functions are solutions to the two phase free boundary problem Du = f x{mº0}      in    W ¶{u>0},                                                                               |Ñu+|2 - |Ñu-|2 = 2M       on    WǶ{u>0}, where f = limfe , in a viscosity sense and in a pointwise sense at regular free boundary points. In addition, we show that the free boundary is smooth and thus limit functions are classical solutions to the free boundary problem, under suitable assumptions. Some of the results obtained are new even in the case feº0. The results in this paper also apply to other combustion models. For instance, models with nonlocal diffusion and/or transport. Several of these applications are discussed here and we get, in some cases, the full regularity of the free boundary.
publishDate 2006
dc.date.none.fl_str_mv 2006-12
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/11336/276544
Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A two phase elliptic singular perturbation problem with a forcing term; Gauthier-Villars/Editions Elsevier; Journal de Mathematiques Pures Et Appliquees; 86; 6; 12-2006; 552-589
0021-7824
CONICET Digital
CONICET
url http://hdl.handle.net/11336/276544
identifier_str_mv Lederman, Claudia Beatriz; Wolanski, Noemi Irene; A two phase elliptic singular perturbation problem with a forcing term; Gauthier-Villars/Editions Elsevier; Journal de Mathematiques Pures Et Appliquees; 86; 6; 12-2006; 552-589
0021-7824
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://www.sciencedirect.com/science/article/pii/S0021782406001280
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.matpur.2006.10.008
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 Gauthier-Villars/Editions Elsevier
publisher.none.fl_str_mv Gauthier-Villars/Editions Elsevier
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 12.952241

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