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dc.contributor.author
Bollati, Julieta
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Gariboldi, Claudia Maricel
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Tarzia, Domingo Alberto
dc.date.available
2022-04-01T20:59:27Z
dc.date.issued
2020-10
dc.identifier.citation
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
dc.identifier.issn
1598-5865
dc.identifier.uri
http://hdl.handle.net/11336/154219
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer Verlag Berlín
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
ELLIPTIC VARIATIONAL INEQUALITIES
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DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS
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MIXED BOUNDARY CONDITIONS
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EXPLICIT SOLUTIONS
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OPTIMALITY CONDITIONS
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Matemática Aplicada
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Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Explicit solutions for distributed, boundary and distributed-boundary elliptic optimal control problems
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2022-03-16T12:39:59Z
dc.identifier.eissn
1865-2085
dc.journal.volume
64
dc.journal.pagination
283-311
dc.journal.pais
Alemania
dc.journal.ciudad
Berlín
dc.description.fil
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
dc.description.fil
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
dc.description.fil
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
dc.journal.title
Journal of Applied Mathematics and Computing
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s12190-020-01355-2
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info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s12190-020-01355-2
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.09261
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