Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems

Autores
Bollati, Julieta; Gariboldi, Claudia Maricel; Tarzia, Domingo Alberto
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider a steady-state heat conduction problem in a multidimensional bounded domainfor the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion 1 of the boundary and a constant heat flux q in the remaining portion2 of the boundary.Moreover, we consider a family of steady-state heat conduction problems with a convective condition on the boundary 1 with heat transfer coefficient α and external temperature b. We obtain explicitly, for a rectangular domain in R2, an annulus in R2 and a spherical shell in R3, the optimal controls, the system states and adjoint states for the following optimal control problems: a distributed control problem on the internal energy g, a boundary optimal control problem on the heat flux q, a boundary optimal control problem on the external temperature b and a distributed-boundary simultaneous optimal control problem on the source g and the flux q. These explicit solutions can be used for testing new numerical methods as a benchmark test. In agreement with theory, it is proved that the system state, adjoint state, optimal controls and optimal values corresponding to the problem with a convective condition on 1 converge, when α → ∞, to the corresponding system state, adjoint state, optimal controls and optimal values that arise from the problem with a temperature condition on 1. Also, we analyze the order of convergence in each case, which turns out to be 1/α being new for these kind of elliptic optimal control problems.
Fil: Bollati, Julieta. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Gariboldi, Claudia Maricel. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
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
ELLIPTIC VARIATIONAL INEQUALITIES
DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS
MIXED BOUNDARY CONDITIONS
EXPLICIT SOLUTIONS
OPTIMALITY CONDITIONS
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:11336/154219
Acceder
id CONICETDig_7b146abb9378aa0b136036aff438ffc9
oai_identifier_str oai:ri.conicet.gov.ar:11336/154219
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problemsBollati, JulietaGariboldi, Claudia MaricelTarzia, Domingo AlbertoELLIPTIC VARIATIONAL INEQUALITIESDISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMSMIXED BOUNDARY CONDITIONSEXPLICIT SOLUTIONSOPTIMALITY CONDITIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider a steady-state heat conduction problem in a multidimensional bounded domainfor the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion 1 of the boundary and a constant heat flux q in the remaining portion2 of the boundary.Moreover, we consider a family of steady-state heat conduction problems with a convective condition on the boundary 1 with heat transfer coefficient α and external temperature b. We obtain explicitly, for a rectangular domain in R2, an annulus in R2 and a spherical shell in R3, the optimal controls, the system states and adjoint states for the following optimal control problems: a distributed control problem on the internal energy g, a boundary optimal control problem on the heat flux q, a boundary optimal control problem on the external temperature b and a distributed-boundary simultaneous optimal control problem on the source g and the flux q. These explicit solutions can be used for testing new numerical methods as a benchmark test. In agreement with theory, it is proved that the system state, adjoint state, optimal controls and optimal values corresponding to the problem with a convective condition on 1 converge, when α → ∞, to the corresponding system state, adjoint state, optimal controls and optimal values that arise from the problem with a temperature condition on 1. Also, we analyze the order of convergence in each case, which turns out to be 1/α being new for these kind of elliptic optimal control problems.Fil: Bollati, Julieta. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaFil: Gariboldi, Claudia Maricel. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; ArgentinaFil: 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; ArgentinaSpringer Verlag Berlín2020-10info: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/11336/154219Bollati, Julieta; Gariboldi, Claudia Maricel; Tarzia, Domingo Alberto; Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems; Springer Verlag Berlín; Journal of Applied Mathematics and Computing; 64; 10-2020; 283-3111598-58651865-2085CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s12190-020-01355-2info:eu-repo/semantics/altIdentifier/doi/10.1007/s12190-020-01355-2info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.09261info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:55:07Zoai:ri.conicet.gov.ar:11336/154219instacron: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 09:55:07.903CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
title Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
spellingShingle Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
Bollati, Julieta
ELLIPTIC VARIATIONAL INEQUALITIES
DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS
MIXED BOUNDARY CONDITIONS
EXPLICIT SOLUTIONS
OPTIMALITY CONDITIONS
title_short Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
title_full Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
title_fullStr Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
title_full_unstemmed Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
title_sort Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
dc.creator.none.fl_str_mv Bollati, Julieta
Gariboldi, Claudia Maricel
Tarzia, Domingo Alberto
author Bollati, Julieta
author_facet Bollati, Julieta
Gariboldi, Claudia Maricel
Tarzia, Domingo Alberto
author_role author
author2 Gariboldi, Claudia Maricel
Tarzia, Domingo Alberto
author2_role author
author
dc.subject.none.fl_str_mv ELLIPTIC VARIATIONAL INEQUALITIES
DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS
MIXED BOUNDARY CONDITIONS
EXPLICIT SOLUTIONS
OPTIMALITY CONDITIONS
topic ELLIPTIC VARIATIONAL INEQUALITIES
DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS
MIXED BOUNDARY CONDITIONS
EXPLICIT SOLUTIONS
OPTIMALITY CONDITIONS
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 steady-state heat conduction problem in a multidimensional bounded domainfor the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion 1 of the boundary and a constant heat flux q in the remaining portion2 of the boundary.Moreover, we consider a family of steady-state heat conduction problems with a convective condition on the boundary 1 with heat transfer coefficient α and external temperature b. We obtain explicitly, for a rectangular domain in R2, an annulus in R2 and a spherical shell in R3, the optimal controls, the system states and adjoint states for the following optimal control problems: a distributed control problem on the internal energy g, a boundary optimal control problem on the heat flux q, a boundary optimal control problem on the external temperature b and a distributed-boundary simultaneous optimal control problem on the source g and the flux q. These explicit solutions can be used for testing new numerical methods as a benchmark test. In agreement with theory, it is proved that the system state, adjoint state, optimal controls and optimal values corresponding to the problem with a convective condition on 1 converge, when α → ∞, to the corresponding system state, adjoint state, optimal controls and optimal values that arise from the problem with a temperature condition on 1. Also, we analyze the order of convergence in each case, which turns out to be 1/α being new for these kind of elliptic optimal control problems.
Fil: Bollati, Julieta. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Fil: Gariboldi, Claudia Maricel. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas, Físico-Químicas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba; Argentina
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 We consider a steady-state heat conduction problem in a multidimensional bounded domainfor the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion 1 of the boundary and a constant heat flux q in the remaining portion2 of the boundary.Moreover, we consider a family of steady-state heat conduction problems with a convective condition on the boundary 1 with heat transfer coefficient α and external temperature b. We obtain explicitly, for a rectangular domain in R2, an annulus in R2 and a spherical shell in R3, the optimal controls, the system states and adjoint states for the following optimal control problems: a distributed control problem on the internal energy g, a boundary optimal control problem on the heat flux q, a boundary optimal control problem on the external temperature b and a distributed-boundary simultaneous optimal control problem on the source g and the flux q. These explicit solutions can be used for testing new numerical methods as a benchmark test. In agreement with theory, it is proved that the system state, adjoint state, optimal controls and optimal values corresponding to the problem with a convective condition on 1 converge, when α → ∞, to the corresponding system state, adjoint state, optimal controls and optimal values that arise from the problem with a temperature condition on 1. Also, we analyze the order of convergence in each case, which turns out to be 1/α being new for these kind of elliptic optimal control problems.
publishDate 2020
dc.date.none.fl_str_mv 2020-10
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/11336/154219
Bollati, Julieta; Gariboldi, Claudia Maricel; Tarzia, Domingo Alberto; Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems; Springer Verlag Berlín; Journal of Applied Mathematics and Computing; 64; 10-2020; 283-311
1598-5865
1865-2085
CONICET Digital
CONICET
url http://hdl.handle.net/11336/154219
identifier_str_mv Bollati, Julieta; Gariboldi, Claudia Maricel; Tarzia, Domingo Alberto; Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems; Springer Verlag Berlín; Journal of Applied Mathematics and Computing; 64; 10-2020; 283-311
1598-5865
1865-2085
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s12190-020-01355-2
info:eu-repo/semantics/altIdentifier/doi/10.1007/s12190-020-01355-2
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.09261
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 Springer Verlag Berlín
publisher.none.fl_str_mv Springer Verlag Berlín
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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