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.
DOI : 10.1051/cocv/2015014
Mots clés : Optimal control problems, Penrose−Fife model, sharp interface
@article{COCV_2016__22_2_473_0,
author = {Colli, Pierluigi and Marinoschi, Gabriela and Rocca, Elisabetta},
title = {Sharp interface control in a {Penrose\ensuremath{-}Fife} model},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {473--499},
publisher = {EDP-Sciences},
volume = {22},
number = {2},
year = {2016},
doi = {10.1051/cocv/2015014},
mrnumber = {3491779},
zbl = {1338.49007},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2015014/}
}
TY - JOUR AU - Colli, Pierluigi AU - Marinoschi, Gabriela AU - Rocca, Elisabetta TI - Sharp interface control in a Penrose−Fife model JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 473 EP - 499 VL - 22 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2015014/ DO - 10.1051/cocv/2015014 LA - en ID - COCV_2016__22_2_473_0 ER -
%0 Journal Article %A Colli, Pierluigi %A Marinoschi, Gabriela %A Rocca, Elisabetta %T Sharp interface control in a Penrose−Fife model %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 473-499 %V 22 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2015014/ %R 10.1051/cocv/2015014 %G en %F COCV_2016__22_2_473_0
Colli, Pierluigi; Marinoschi, Gabriela; Rocca, Elisabetta. Sharp interface control in a Penrose−Fife model. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 2, pp. 473-499. doi : 10.1051/cocv/2015014. http://www.numdam.org/articles/10.1051/cocv/2015014/
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