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.
Optimal control for a phase field system with a possibly singular potential / P. Colli, G. Gilardi, G. Marinoschi, E. Rocca. - In: MATHEMATICAL CONTROL AND RELATED FIELDS. - ISSN 2156-8472. - 6:1(2016), pp. 95-112. [10.3934/mcrf.2016.6.95]
Optimal control for a phase field system with a possibly singular potential
E. Rocca
2016
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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