Uniqueness of solution to a free boundary problem from combustion

Autores
Lederman, Claudia Beatriz; Vázquez, Juan Luis; Wolanski, Noemi Irene
Año de publicación
2001
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, defined in a domain D ⊂ RN × (0, T) and such that ∆u +Xai uxi − ut = 0 in D∩{u > 0}. We also assume that the interior boundary of the positivity set, D ∩ ∂{u > 0}, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied: u = 0, −∂u/∂ν = C. Here ν denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
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
Fil: Vázquez, Juan Luis. Universidad Autónoma de Madrid; España
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
FREE-BOUNDARY PROBLEM
COMBUSTION
HEAT EQUATION
UNIQUENESS
CLASSICAL SOLUTION
VISCOSITY SOLUTION
LIMIT SOLUTION
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:11336/151909
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/151909
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Uniqueness of solution to a free boundary problem from combustionLederman, Claudia BeatrizVázquez, Juan LuisWolanski, Noemi IreneFREE-BOUNDARY PROBLEMCOMBUSTIONHEAT EQUATIONUNIQUENESSCLASSICAL SOLUTIONVISCOSITY SOLUTIONLIMIT SOLUTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, defined in a domain D ⊂ RN × (0, T) and such that ∆u +Xai uxi − ut = 0 in D∩{u > 0}. We also assume that the interior boundary of the positivity set, D ∩ ∂{u > 0}, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied: u = 0, −∂u/∂ν = C. Here ν denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.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"; ArgentinaFil: Vázquez, Juan Luis. Universidad Autónoma de Madrid; EspañaFil: 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 Society2001-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/151909Lederman, Claudia Beatriz; Vázquez, Juan Luis; Wolanski, Noemi Irene; Uniqueness of solution to a free boundary problem from combustion; American Mathematical Society; Transactions of the American Mathematical Society; 353; 2; 4-2001; 655-6920002-99471088-6850CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2001-353-02/home.htmlinfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2001-353-02/S0002-9947-00-02663-5/S0002-9947-00-02663-5.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:49:04Zoai:ri.conicet.gov.ar:11336/151909instacron: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 09:49:04.941CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Uniqueness of solution to a free boundary problem from combustion
title Uniqueness of solution to a free boundary problem from combustion
spellingShingle Uniqueness of solution to a free boundary problem from combustion
Lederman, Claudia Beatriz
FREE-BOUNDARY PROBLEM
COMBUSTION
HEAT EQUATION
UNIQUENESS
CLASSICAL SOLUTION
VISCOSITY SOLUTION
LIMIT SOLUTION
title_short Uniqueness of solution to a free boundary problem from combustion
title_full Uniqueness of solution to a free boundary problem from combustion
title_fullStr Uniqueness of solution to a free boundary problem from combustion
title_full_unstemmed Uniqueness of solution to a free boundary problem from combustion
title_sort Uniqueness of solution to a free boundary problem from combustion
dc.creator.none.fl_str_mv Lederman, Claudia Beatriz
Vázquez, Juan Luis
Wolanski, Noemi Irene
author Lederman, Claudia Beatriz
author_facet Lederman, Claudia Beatriz
Vázquez, Juan Luis
Wolanski, Noemi Irene
author_role author
author2 Vázquez, Juan Luis
Wolanski, Noemi Irene
author2_role author
author
dc.subject.none.fl_str_mv FREE-BOUNDARY PROBLEM
COMBUSTION
HEAT EQUATION
UNIQUENESS
CLASSICAL SOLUTION
VISCOSITY SOLUTION
LIMIT SOLUTION
topic FREE-BOUNDARY PROBLEM
COMBUSTION
HEAT EQUATION
UNIQUENESS
CLASSICAL SOLUTION
VISCOSITY SOLUTION
LIMIT SOLUTION
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 investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, defined in a domain D ⊂ RN × (0, T) and such that ∆u +Xai uxi − ut = 0 in D∩{u > 0}. We also assume that the interior boundary of the positivity set, D ∩ ∂{u > 0}, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied: u = 0, −∂u/∂ν = C. Here ν denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
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
Fil: Vázquez, Juan Luis. Universidad Autónoma de Madrid; España
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 We investigate the uniqueness and agreement between different kinds of solutions for a free boundary problem in heat propagation that in classical terms is formulated as follows: to find a continuous function u(x, t) ≥ 0, defined in a domain D ⊂ RN × (0, T) and such that ∆u +Xai uxi − ut = 0 in D∩{u > 0}. We also assume that the interior boundary of the positivity set, D ∩ ∂{u > 0}, so-called free boundary, is a regular hypersurface on which the following conditions are satisfied: u = 0, −∂u/∂ν = C. Here ν denotes outward unit spatial normal to the free boundary. In addition, initial data are specified, as well as either Dirichlet or Neumann data on the parabolic boundary of D. This problem arises in combustion theory as a limit situation in the propagation of premixed flames (high activation energy limit). The problem admits classical solutions only for good data and for small times. Several generalized concepts of solution have been proposed, among them the concepts of limit solution and viscosity solution. We investigate conditions under which the three concepts agree and produce a unique solution.
publishDate 2001
dc.date.none.fl_str_mv 2001-04
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/11336/151909
Lederman, Claudia Beatriz; Vázquez, Juan Luis; Wolanski, Noemi Irene; Uniqueness of solution to a free boundary problem from combustion; American Mathematical Society; Transactions of the American Mathematical Society; 353; 2; 4-2001; 655-692
0002-9947
1088-6850
CONICET Digital
CONICET
url http://hdl.handle.net/11336/151909
identifier_str_mv Lederman, Claudia Beatriz; Vázquez, Juan Luis; Wolanski, Noemi Irene; Uniqueness of solution to a free boundary problem from combustion; American Mathematical Society; Transactions of the American Mathematical Society; 353; 2; 4-2001; 655-692
0002-9947
1088-6850
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.ams.org/journals/tran/2001-353-02/home.html
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/tran/2001-353-02/S0002-9947-00-02663-5/S0002-9947-00-02663-5.pdf
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 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
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score 13.13397

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