Distributed optimal control problems for phase field systems with singular potential

In this paper we review some results obtained for a distributed control problem regarding a class of phase field systems of Caginalp type with logarithmic potential. The aim of the control problem is forcing the location of the diffuse interface to be as close as possible to a prescribed set. However, due to some discontinuity in the cost functional, we have to regularize it and solve the related control problem for the approximation. We discuss the necessary optimality conditions.