Optimal distributed control for a coupled phase-field system (Q2669217)

This paper considered a distributed optimal control for a coupled phase-field system. The control acts in the whole domain and the objective functional is of tracking type. The authors proved the existence of a weak solution to the governing state equantion and the existence of a solution to the nonlinear optimal control problem. The differentiability of the control-to-state mapping was studied which allows to derive a first order necessary optimality condition with the aid of an adjoint state system.