Ciro D'Apice, Umberto De Maio, Peter I. Kogut, Rosanna Manzo
Abstract:
We study an optimal control problem (OCP) associated to a linear elliptic
equation
.
The characteristic feature of this control object is the fact that the
matrix
is skew-symmetric and belongs to
-space (rather
than
.
We adopt a symmetric
positive defined matrix
as control in
.
In spite of the fact that the equations of this type can exhibit non-uniqueness
of weak solutions, we prove that the corresponding OCP, under rather general
assumptions on the class of admissible controls, is well-posed and admits a
nonempty set of solutions. The main trick we apply to the proof of the existence
result is the approximation of the original OCP by regularized OCPs in perforated
domains with fictitious boundary controls on the holes.
Submitted May 5, 2014. Published July 30, 2014.
Math Subject Classifications: 49J20, 35J57, 49J45, 35J75.
Key Words: Elliptic equation; control in coefficients; variational convergence;
fictitious control.
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Ciro D'Apice Department of Information Engineering Electrical Engineering and Applied Mathematics University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Salerno, Italy email: cdapice@unisa.it | |
Umberto De Maio Dipartimento di Matematica e Applicazioni R. Caccioppoli, Universitá degli Studi di Napoli Federico II, Complesso Monte S. Angelo via Cintia, 80126 Napoli, Italy email: udemaio@unina.it | |
Peter I. Kogut Department of Differential Equations Dnipropetrovsk National University Gagarin av., 72, 49010 Dnipropetrovsk, Ukraine email: p.kogut@i.ua | |
Rosanna Manzo Department of Information Engineering Electrical Engineering and Applied Mathematics University of Salerno, Via Giovanni Paolo II 132, 84084 Fisciano, Salerno, Italy email: rmanzo@unisa.it |
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