Convergence of simultaneous distributed-boundary parabolic optimal control problems

Autores
Tarzia, Domingo Alberto; Bollo, Carolina María; Gariboldi, Claudia Maricel
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a heat conduction problem S with mixed boundary conditions in a n-dimensional domain Ω with regular boundary Γ and a family of problems Sα, where the parameter α > 0 is the heat transfer coefficient on the portion of the boundary Γ1 . In relation to these state systems, we formulate simultaneous distributed-boundary optimal control problems on the internal energy g and the heat flux q on the complementary portion of the boundary Γ2 . We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system and the adjoint states when the heat transfer coefficient α goes to infinity. Finally, we prove estimations between the simultaneous distributed-boundary optimal control and the distributed optimal control problem studied in a previous paper of the first author.
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral; Argentina
Fil: Bollo, Carolina María. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; Argentina
Fil: Gariboldi, Claudia Maricel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; Argentina
Materia
EXISTENCE AND UNIQUENESS
MIXED BOUNDARY CON-DITIONS
OPTIMAL CONTROL
OPTIMALITY CONDITIONS
PARABOLIC VARIATIONAL EQUALITIES
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:11336/150582
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/150582
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Convergence of simultaneous distributed-boundary parabolic optimal control problemsTarzia, Domingo AlbertoBollo, Carolina MaríaGariboldi, Claudia MaricelEXISTENCE AND UNIQUENESSMIXED BOUNDARY CON-DITIONSOPTIMAL CONTROLOPTIMALITY CONDITIONSPARABOLIC VARIATIONAL EQUALITIEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a heat conduction problem S with mixed boundary conditions in a n-dimensional domain Ω with regular boundary Γ and a family of problems Sα, where the parameter α > 0 is the heat transfer coefficient on the portion of the boundary Γ1 . In relation to these state systems, we formulate simultaneous distributed-boundary optimal control problems on the internal energy g and the heat flux q on the complementary portion of the boundary Γ2 . We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system and the adjoint states when the heat transfer coefficient α goes to infinity. Finally, we prove estimations between the simultaneous distributed-boundary optimal control and the distributed optimal control problem studied in a previous paper of the first author.Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral; ArgentinaFil: Bollo, Carolina María. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; ArgentinaFil: Gariboldi, Claudia Maricel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; ArgentinaAmerican Institute of Mathematical Sciences2020-12info: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/11336/150582Tarzia, Domingo Alberto; Bollo, Carolina María; Gariboldi, Claudia Maricel; Convergence of simultaneous distributed-boundary parabolic optimal control problems; American Institute of Mathematical Sciences; Evolution Equations and Control Theory; 9; 4; 12-2020; 1187-12012163-24722163-2480CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.3934/eect.2020045info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/eect.2020045info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1912.09157info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:41Zoai:ri.conicet.gov.ar:11336/150582instacron: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 09:55:41.395CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Convergence of simultaneous distributed-boundary parabolic optimal control problems
title Convergence of simultaneous distributed-boundary parabolic optimal control problems
spellingShingle Convergence of simultaneous distributed-boundary parabolic optimal control problems
Tarzia, Domingo Alberto
EXISTENCE AND UNIQUENESS
MIXED BOUNDARY CON-DITIONS
OPTIMAL CONTROL
OPTIMALITY CONDITIONS
PARABOLIC VARIATIONAL EQUALITIES
title_short Convergence of simultaneous distributed-boundary parabolic optimal control problems
title_full Convergence of simultaneous distributed-boundary parabolic optimal control problems
title_fullStr Convergence of simultaneous distributed-boundary parabolic optimal control problems
title_full_unstemmed Convergence of simultaneous distributed-boundary parabolic optimal control problems
title_sort Convergence of simultaneous distributed-boundary parabolic optimal control problems
dc.creator.none.fl_str_mv Tarzia, Domingo Alberto
Bollo, Carolina María
Gariboldi, Claudia Maricel
author Tarzia, Domingo Alberto
author_facet Tarzia, Domingo Alberto
Bollo, Carolina María
Gariboldi, Claudia Maricel
author_role author
author2 Bollo, Carolina María
Gariboldi, Claudia Maricel
author2_role author
author
dc.subject.none.fl_str_mv EXISTENCE AND UNIQUENESS
MIXED BOUNDARY CON-DITIONS
OPTIMAL CONTROL
OPTIMALITY CONDITIONS
PARABOLIC VARIATIONAL EQUALITIES
topic EXISTENCE AND UNIQUENESS
MIXED BOUNDARY CON-DITIONS
OPTIMAL CONTROL
OPTIMALITY CONDITIONS
PARABOLIC VARIATIONAL EQUALITIES
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 a heat conduction problem S with mixed boundary conditions in a n-dimensional domain Ω with regular boundary Γ and a family of problems Sα, where the parameter α > 0 is the heat transfer coefficient on the portion of the boundary Γ1 . In relation to these state systems, we formulate simultaneous distributed-boundary optimal control problems on the internal energy g and the heat flux q on the complementary portion of the boundary Γ2 . We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system and the adjoint states when the heat transfer coefficient α goes to infinity. Finally, we prove estimations between the simultaneous distributed-boundary optimal control and the distributed optimal control problem studied in a previous paper of the first author.
Fil: Tarzia, Domingo Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Austral; Argentina
Fil: Bollo, Carolina María. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; Argentina
Fil: Gariboldi, Claudia Maricel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Fisicoquímicas y Naturales. Departamento de Matemática; Argentina
description We consider a heat conduction problem S with mixed boundary conditions in a n-dimensional domain Ω with regular boundary Γ and a family of problems Sα, where the parameter α > 0 is the heat transfer coefficient on the portion of the boundary Γ1 . In relation to these state systems, we formulate simultaneous distributed-boundary optimal control problems on the internal energy g and the heat flux q on the complementary portion of the boundary Γ2 . We obtain existence and uniqueness of the optimal controls, the first order optimality conditions in terms of the adjoint state and the convergence of the optimal controls, the system and the adjoint states when the heat transfer coefficient α goes to infinity. Finally, we prove estimations between the simultaneous distributed-boundary optimal control and the distributed optimal control problem studied in a previous paper of the first author.
publishDate 2020
dc.date.none.fl_str_mv 2020-12
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/11336/150582
Tarzia, Domingo Alberto; Bollo, Carolina María; Gariboldi, Claudia Maricel; Convergence of simultaneous distributed-boundary parabolic optimal control problems; American Institute of Mathematical Sciences; Evolution Equations and Control Theory; 9; 4; 12-2020; 1187-1201
2163-2472
2163-2480
CONICET Digital
CONICET
url http://hdl.handle.net/11336/150582
identifier_str_mv Tarzia, Domingo Alberto; Bollo, Carolina María; Gariboldi, Claudia Maricel; Convergence of simultaneous distributed-boundary parabolic optimal control problems; American Institute of Mathematical Sciences; Evolution Equations and Control Theory; 9; 4; 12-2020; 1187-1201
2163-2472
2163-2480
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.3934/eect.2020045
info:eu-repo/semantics/altIdentifier/url/https://www.aimsciences.org/article/doi/10.3934/eect.2020045
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1912.09157
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 American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
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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