Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source

Autores
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Villa Saravia, Luis Tadeo
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a non-uniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term. Explicit solutions independent of the space or temporal variables, solutions with separated variables and solutions by an integral representation depending on the heat flux at the boundary are given. The controlling effects of the source term are analyzed by comparing the asymptotic temporal behavior of solutions corresponding to the same problem with and without source term. Finally, a relationship between the problem considered here with another non-classical problem for the heat equation is established, and explicit solutions for this second problem are also obtained. In this article, we give explicit solutions and analyze how to control them through the source term for several non-classical heat equation problems. In addition, our results enable us to compute the asymptotic temporal behavior of the heat flux at the boundary for each explicit solution obtained. As a consequence of our study, several solved non-classical problems for the heat equation that can be used for testing new numerical methods are given.
Fil: Ceretani, Andrea Noemí. 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 Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Villa Saravia, Luis Tadeo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; Argentina
Materia
EXPLICIT SOLUTIONS
NON-CLASSICAL HEAT EQUATION
NONLINEAR HEAT CONDUCTION PROBLEMS
VOLTERRA INTEGRAL EQUATIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/121273
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat sourceCeretani, Andrea NoemíTarzia, Domingo AlbertoVilla Saravia, Luis TadeoEXPLICIT SOLUTIONSNON-CLASSICAL HEAT EQUATIONNONLINEAR HEAT CONDUCTION PROBLEMSVOLTERRA INTEGRAL EQUATIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a non-uniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term. Explicit solutions independent of the space or temporal variables, solutions with separated variables and solutions by an integral representation depending on the heat flux at the boundary are given. The controlling effects of the source term are analyzed by comparing the asymptotic temporal behavior of solutions corresponding to the same problem with and without source term. Finally, a relationship between the problem considered here with another non-classical problem for the heat equation is established, and explicit solutions for this second problem are also obtained. In this article, we give explicit solutions and analyze how to control them through the source term for several non-classical heat equation problems. In addition, our results enable us to compute the asymptotic temporal behavior of the heat flux at the boundary for each explicit solution obtained. As a consequence of our study, several solved non-classical problems for the heat equation that can be used for testing new numerical methods are given.Fil: Ceretani, Andrea Noemí. 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 Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; ArgentinaFil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Villa Saravia, Luis Tadeo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; ArgentinaSpringer2015-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/121273Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Villa Saravia, Luis Tadeo; Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source; Springer; Boundary Value Problems; 2015; 1; 12-2015; 1-261687-27621687-2770CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1186/s13661-015-0416-3info:eu-repo/semantics/altIdentifier/url/https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-015-0416-3info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:12:40Zoai:ri.conicet.gov.ar:11336/121273instacron: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 10:12:41.123CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
title Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
spellingShingle Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
Ceretani, Andrea Noemí
EXPLICIT SOLUTIONS
NON-CLASSICAL HEAT EQUATION
NONLINEAR HEAT CONDUCTION PROBLEMS
VOLTERRA INTEGRAL EQUATIONS
title_short Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
title_full Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
title_fullStr Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
title_full_unstemmed Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
title_sort Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source
dc.creator.none.fl_str_mv Ceretani, Andrea Noemí
Tarzia, Domingo Alberto
Villa Saravia, Luis Tadeo
author Ceretani, Andrea Noemí
author_facet Ceretani, Andrea Noemí
Tarzia, Domingo Alberto
Villa Saravia, Luis Tadeo
author_role author
author2 Tarzia, Domingo Alberto
Villa Saravia, Luis Tadeo
author2_role author
author
dc.subject.none.fl_str_mv EXPLICIT SOLUTIONS
NON-CLASSICAL HEAT EQUATION
NONLINEAR HEAT CONDUCTION PROBLEMS
VOLTERRA INTEGRAL EQUATIONS
topic EXPLICIT SOLUTIONS
NON-CLASSICAL HEAT EQUATION
NONLINEAR HEAT CONDUCTION PROBLEMS
VOLTERRA INTEGRAL EQUATIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a non-uniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term. Explicit solutions independent of the space or temporal variables, solutions with separated variables and solutions by an integral representation depending on the heat flux at the boundary are given. The controlling effects of the source term are analyzed by comparing the asymptotic temporal behavior of solutions corresponding to the same problem with and without source term. Finally, a relationship between the problem considered here with another non-classical problem for the heat equation is established, and explicit solutions for this second problem are also obtained. In this article, we give explicit solutions and analyze how to control them through the source term for several non-classical heat equation problems. In addition, our results enable us to compute the asymptotic temporal behavior of the heat flux at the boundary for each explicit solution obtained. As a consequence of our study, several solved non-classical problems for the heat equation that can be used for testing new numerical methods are given.
Fil: Ceretani, Andrea Noemí. 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 Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina
Fil: Villa Saravia, Luis Tadeo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Investigaciones para la Industria Química. Universidad Nacional de Salta. Facultad de Ingeniería. Instituto de Investigaciones para la Industria Química; Argentina
description A non-classical initial and boundary value problem for a non-homogeneous one-dimensional heat equation for a semi-infinite material with a zero temperature boundary condition is studied. It is not a standard heat conduction problem because a non-uniform heat source dependent on the heat flux at the boundary is considered. The purpose of this article is to find explicit solutions and analyze how to control their asymptotic temporal behavior through the source term. Explicit solutions independent of the space or temporal variables, solutions with separated variables and solutions by an integral representation depending on the heat flux at the boundary are given. The controlling effects of the source term are analyzed by comparing the asymptotic temporal behavior of solutions corresponding to the same problem with and without source term. Finally, a relationship between the problem considered here with another non-classical problem for the heat equation is established, and explicit solutions for this second problem are also obtained. In this article, we give explicit solutions and analyze how to control them through the source term for several non-classical heat equation problems. In addition, our results enable us to compute the asymptotic temporal behavior of the heat flux at the boundary for each explicit solution obtained. As a consequence of our study, several solved non-classical problems for the heat equation that can be used for testing new numerical methods are given.
publishDate 2015
dc.date.none.fl_str_mv 2015-12
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/11336/121273
Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Villa Saravia, Luis Tadeo; Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source; Springer; Boundary Value Problems; 2015; 1; 12-2015; 1-26
1687-2762
1687-2770
CONICET Digital
CONICET
url http://hdl.handle.net/11336/121273
identifier_str_mv Ceretani, Andrea Noemí; Tarzia, Domingo Alberto; Villa Saravia, Luis Tadeo; Explicit solutions for a non-classical heat conduction problem for a semi-infinite strip with a non-uniform heat source; Springer; Boundary Value Problems; 2015; 1; 12-2015; 1-26
1687-2762
1687-2770
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1186/s13661-015-0416-3
info:eu-repo/semantics/altIdentifier/url/https://boundaryvalueproblems.springeropen.com/articles/10.1186/s13661-015-0416-3
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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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