Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind

Autores
Boukrouche, Mahdi; Tarzia, Domingo Alberto
Año de publicación
2011
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let ug be the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between µug1 + (1 − µ)ug2 and uµg1+(1−µ)g2 for µ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated with the Newton law, and of another optimal control problem associated with a Dirichlet boundary condition. We prove also, when h → +∞, the strong convergence of the optimal controls and states associated with this family of optimal control problems with the Newton law to that of the optimal control problem associated with a Dirichlet boundary condition.
Fil: Boukrouche, Mahdi. Universite Lyon 2; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
Parabolic variational inequalities
existence and uniqueness
Optimal control
Convergence
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:11336/280808
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/280808
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network_name_str CONICET Digital (CONICET)
spelling Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kindBoukrouche, MahdiTarzia, Domingo AlbertoParabolic variational inequalitiesexistence and uniquenessOptimal controlConvergencehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let ug be the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between µug1 + (1 − µ)ug2 and uµg1+(1−µ)g2 for µ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated with the Newton law, and of another optimal control problem associated with a Dirichlet boundary condition. We prove also, when h → +∞, the strong convergence of the optimal controls and states associated with this family of optimal control problems with the Newton law to that of the optimal control problem associated with a Dirichlet boundary condition.Fil: Boukrouche, Mahdi. Universite Lyon 2; FranciaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaPergamon-Elsevier Science Ltd2011-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/280808Boukrouche, Mahdi; Tarzia, Domingo Alberto; Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 12; 4; 3-2011; 2211-22241468-1218CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S1468121811000046info:eu-repo/semantics/altIdentifier/doi/10.1016/j.nonrwa.2011.01.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:02:57Zoai:ri.conicet.gov.ar:11336/280808instacron: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:34982026-02-26 10:02:58.195CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
title Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
spellingShingle Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
Boukrouche, Mahdi
Parabolic variational inequalities
existence and uniqueness
Optimal control
Convergence
title_short Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
title_full Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
title_fullStr Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
title_full_unstemmed Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
title_sort Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind
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 Parabolic variational inequalities
existence and uniqueness
Optimal control
Convergence
topic Parabolic variational inequalities
existence and uniqueness
Optimal control
Convergence
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let ug be the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between µug1 + (1 − µ)ug2 and uµg1+(1−µ)g2 for µ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated with the Newton law, and of another optimal control problem associated with a Dirichlet boundary condition. We prove also, when h → +∞, the strong convergence of the optimal controls and states associated with this family of optimal control problems with the Newton law to that of the optimal control problem associated with a Dirichlet boundary condition.
Fil: Boukrouche, Mahdi. Universite Lyon 2; Francia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description Let ug be the unique solution of a parabolic variational inequality of second kind, with a given g. Using a regularization method, we prove, for all g1 and g2, a monotony property between µug1 + (1 − µ)ug2 and uµg1+(1−µ)g2 for µ ∈ [0, 1]. This allowed us to prove the existence and uniqueness results to a family of optimal control problems over g for each heat transfer coefficient h > 0, associated with the Newton law, and of another optimal control problem associated with a Dirichlet boundary condition. We prove also, when h → +∞, the strong convergence of the optimal controls and states associated with this family of optimal control problems with the Newton law to that of the optimal control problem associated with a Dirichlet boundary condition.
publishDate 2011
dc.date.none.fl_str_mv 2011-03
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/11336/280808
Boukrouche, Mahdi; Tarzia, Domingo Alberto; Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 12; 4; 3-2011; 2211-2224
1468-1218
CONICET Digital
CONICET
url http://hdl.handle.net/11336/280808
identifier_str_mv Boukrouche, Mahdi; Tarzia, Domingo Alberto; Existence, uniqueness, and convergence of optimal control problems associated with parabolic variational inequalities of the second kind; Pergamon-Elsevier Science Ltd; Nonlinear Analysis-real World Applications; 12; 4; 3-2011; 2211-2224
1468-1218
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.sciencedirect.com/science/article/abs/pii/S1468121811000046
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.nonrwa.2011.01.003
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 Pergamon-Elsevier Science Ltd
publisher.none.fl_str_mv Pergamon-Elsevier Science Ltd
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 13.176822

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