Volume 22, Number 2, April-June 2016
|Page(s)||473 - 499|
|Published online||18 March 2016|
Sharp interface control in a Penrose−Fife model
Dipartimento di Matematica, Università degli Studi di
Pavia, Via Ferrata
2 Institute of Mathematical Statistics and Applied Mathematics, Calea 13 Septembrie No.13, Sector 5, 050711, Bucharest, Romania
3 Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany
4 Dipartimento di Matematica, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy
Revised: 3 December 2014
In this paper we study a singular control problem for a system of PDEs describing a phase-field model of Penrose−Fife type. The main novelty of this contribution consists in the idea of forcing a sharp interface separation between the states of the system by using heat sources distributed in the domain and at the boundary. We approximate the singular cost functional with a regular one, which is based on the Legendre−Fenchel relations. Then, we obtain a regularized control problem for which we compute the first order optimality conditions using an adapted penalization technique. The proof of some convergence results and the passage to the limit in these optimality conditions lead to the characterization of the desired optimal controller.
Mathematics Subject Classification: 49J20 / 82B26 / 90C46
Key words: Optimal control problems / Penrose−Fife model / sharp interface
© EDP Sciences, SMAI 2016
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