Optimal control for a phase field system with a possibly singular potential
Pierluigi Colli, Gianni Gilardi, Gabriela Marinoschi, Elisabetta Rocca · Mathematical Control and Related Fields · 2016
In this paper we study a distributed control problem for a phase field system of Caginalp type withlogarithmic potential. The main aim of this work would be to force the location of the diffuse interfaceto be as close as possible to a prescribed set. However, due to the discontinuous character of thecost 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.