  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.
