Optimal distributed control for a coupled phase-field system

Abstract

<p style='text-indent:20px;'>Our aim is to consider a distributed optimal control problem for a coupled phase-field system which was introduced by Cahn and Novick-Cohen. First, we establish that the existence of a weak solution, in particular, we also obtain that a strong solution is uniqueness. Then the existence of optimal controls is proved. Finally we derive that the control-to-state operator is Fréchet differentiable and the first-order necessary optimality conditions involving the adjoint system are discussed as well.</p>