dc.creator | Bollati, Julieta | |
dc.creator | Gariboldi, Claudia Maricel | |
dc.creator | Tarzia, Domingo Alberto | |
dc.date.accessioned | 2022-04-01T20:59:27Z | |
dc.date.accessioned | 2022-10-15T05:33:02Z | |
dc.date.available | 2022-04-01T20:59:27Z | |
dc.date.available | 2022-10-15T05:33:02Z | |
dc.date.created | 2022-04-01T20:59:27Z | |
dc.date.issued | 2020-10 | |
dc.identifier | 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 | 1598-5865 | |
dc.identifier | http://hdl.handle.net/11336/154219 | |
dc.identifier | 1865-2085 | |
dc.identifier | CONICET Digital | |
dc.identifier | CONICET | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/4350201 | |
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.language | eng | |
dc.publisher | Springer Verlag Berlín | |
dc.relation | info:eu-repo/semantics/altIdentifier/url/http://link.springer.com/10.1007/s12190-020-01355-2 | |
dc.relation | info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s12190-020-01355-2 | |
dc.relation | info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.09261 | |
dc.rights | https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ | |
dc.rights | info:eu-repo/semantics/openAccess | |
dc.subject | ELLIPTIC VARIATIONAL INEQUALITIES | |
dc.subject | DISTRIBUTED AND BOUNDARY OPTIMAL CONTROL PROBLEMS | |
dc.subject | MIXED BOUNDARY CONDITIONS | |
dc.subject | EXPLICIT SOLUTIONS | |
dc.subject | OPTIMALITY CONDITIONS | |
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 | |