Optimal control of a phase field model for solidification

A free boundary value problem is considered modeling solidification of a liquid by making use of the phase field approach as it was introduced by G. Caginalp [1] and others. Existence and uniqueness is proved as well as stability under mild assumptions. But the main goal of this paper is to establish results for the distributed optimal control of the phase field equations. Besides the existence of an optimal control necessary optimality conditions will be proved and some uniqueness results will be obtained.