Optimal control for a phase field system with a possibly singular potential

Pierluigi Colli; Gianni Gilardi; Gabriela  Marinoschi; Elisabetta Rocca

doi:10.3934/mcrf.2016.6.95

Article Contents

2016, Volume 6, Issue 1: 95-112. Doi: 10.3934/mcrf.2016.6.95

This issue Previous Article Optimal sampled-data control, and generalizations on time scales Next Article A relaxation result for state constrained inclusions in infinite dimension

Optimal control for a phase field system with a possibly singular potential

1.
Dipartimento di Matematica "F. Casorati", Università di Pavia, Via Ferrata 1, 27100 Pavia
2.
"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy (ISMMA), Calea 13 Septembrie 13, 050711 Bucharest
3.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin

Received: October 2014

Revised: July 2015

Published: March 2016

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Abstract

In this paper we study a distributed control problem for a phase field system of Caginalp type with logarithmic potential. The main aim of this work would be to force the location of the diffuse interface to be as close as possible to a prescribed set. However, due to the discontinuous character of the cost functional, we have to approximate it by a regular one and, in this case, we solve the associated control problem and derive the related first order necessary optimality conditions.

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Mathematics Subject Classification: Primary: 49J20; Secondary: 35K55, 49K20, 80A22.

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