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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/31128
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:24:17Zoai: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:34982025-09-29 10:24:17.518CONICET 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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1844614239220662272 |
score |
13.070432 |