Global solution to a non-classical heat problem in the semi-space r+ × rn−1

Autores
Boukrouche, Mahdi; Tarzia, Domingo Alberto
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider the non-classical heat equation in the n-dimensional domain D = R+ × Rn−1 for which the internal energy supply depends on the heat flux on the boundary S = ∂D. The problem is motivated by the modeling of temperature regulation in the medium. Using the Green function for the domain D, the solution is found for an integral representation depending on the heat flux V on S which is an additional unknown of the problem. We obtain that V must satisfy a Volterra integral equation of second kind at time t with a parameter in Rn−1. Under some conditions on data, we show that there exists a unique local solution which can be extended globally in time. This work generalizes the results obtained in the one-dimensional case
Fil: Boukrouche, Mahdi. Universite Lyon 2; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
Non-Classical Heat Equation
Global 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:11336/31128
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Global solution to a non-classical heat problem in the semi-space r+ × rn−1Boukrouche, MahdiTarzia, Domingo AlbertoNon-Classical Heat EquationGlobal Solutionhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider the non-classical heat equation in the n-dimensional domain D = R+ × Rn−1 for which the internal energy supply depends on the heat flux on the boundary S = ∂D. The problem is motivated by the modeling of temperature regulation in the medium. Using the Green function for the domain D, the solution is found for an integral representation depending on the heat flux V on S which is an additional unknown of the problem. We obtain that V must satisfy a Volterra integral equation of second kind at time t with a parameter in Rn−1. Under some conditions on data, we show that there exists a unique local solution which can be extended globally in time. This work generalizes the results obtained in the one-dimensional caseFil: Boukrouche, Mahdi. Universite Lyon 2; FranciaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaUniv Press Inc2014-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/31128Tarzia, Domingo Alberto; Boukrouche, Mahdi; Global solution to a non-classical heat problem in the semi-space r+ × rn−1; Univ Press Inc; Quarterly Of Applied Mathematics; 72; 2; 6-2014; 347-3610033-569XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1090/S0033-569X-2014-01344-1info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/qam/2014-72-02/S0033-569X-2014-01344-1/home.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:29:47Zoai:ri.conicet.gov.ar:11336/31128instacron: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:34982025-10-29 12:29:47.866CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Global solution to a non-classical heat problem in the semi-space r+ × rn−1
title Global solution to a non-classical heat problem in the semi-space r+ × rn−1
spellingShingle Global solution to a non-classical heat problem in the semi-space r+ × rn−1
Boukrouche, Mahdi
Non-Classical Heat Equation
Global Solution
title_short Global solution to a non-classical heat problem in the semi-space r+ × rn−1
title_full Global solution to a non-classical heat problem in the semi-space r+ × rn−1
title_fullStr Global solution to a non-classical heat problem in the semi-space r+ × rn−1
title_full_unstemmed Global solution to a non-classical heat problem in the semi-space r+ × rn−1
title_sort Global solution to a non-classical heat problem in the semi-space r+ × rn−1
dc.creator.none.fl_str_mv Boukrouche, Mahdi
Tarzia, Domingo Alberto
author Boukrouche, Mahdi
author_facet Boukrouche, Mahdi
Tarzia, Domingo Alberto
author_role author
author2 Tarzia, Domingo Alberto
author2_role author
dc.subject.none.fl_str_mv Non-Classical Heat Equation
Global Solution
topic Non-Classical Heat Equation
Global 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 consider the non-classical heat equation in the n-dimensional domain D = R+ × Rn−1 for which the internal energy supply depends on the heat flux on the boundary S = ∂D. The problem is motivated by the modeling of temperature regulation in the medium. Using the Green function for the domain D, the solution is found for an integral representation depending on the heat flux V on S which is an additional unknown of the problem. We obtain that V must satisfy a Volterra integral equation of second kind at time t with a parameter in Rn−1. Under some conditions on data, we show that there exists a unique local solution which can be extended globally in time. This work generalizes the results obtained in the one-dimensional case
Fil: Boukrouche, Mahdi. Universite Lyon 2; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Cs.empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We consider the non-classical heat equation in the n-dimensional domain D = R+ × Rn−1 for which the internal energy supply depends on the heat flux on the boundary S = ∂D. The problem is motivated by the modeling of temperature regulation in the medium. Using the Green function for the domain D, the solution is found for an integral representation depending on the heat flux V on S which is an additional unknown of the problem. We obtain that V must satisfy a Volterra integral equation of second kind at time t with a parameter in Rn−1. Under some conditions on data, we show that there exists a unique local solution which can be extended globally in time. This work generalizes the results obtained in the one-dimensional case
publishDate 2014
dc.date.none.fl_str_mv 2014-06
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/11336/31128
Tarzia, Domingo Alberto; Boukrouche, Mahdi; Global solution to a non-classical heat problem in the semi-space r+ × rn−1; Univ Press Inc; Quarterly Of Applied Mathematics; 72; 2; 6-2014; 347-361
0033-569X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/31128
identifier_str_mv Tarzia, Domingo Alberto; Boukrouche, Mahdi; Global solution to a non-classical heat problem in the semi-space r+ × rn−1; Univ Press Inc; Quarterly Of Applied Mathematics; 72; 2; 6-2014; 347-361
0033-569X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1090/S0033-569X-2014-01344-1
info:eu-repo/semantics/altIdentifier/url/http://www.ams.org/journals/qam/2014-72-02/S0033-569X-2014-01344-1/home.html
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 Univ Press Inc
publisher.none.fl_str_mv Univ Press Inc
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 12.589754

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