Optimal Control of the Obstacle for a Parabolic Variational Inequality

An optimal control problem for a parabolic obstacle variational inequality is considered. The obstacle in L2 0 T H2 ∩ H1 0 with ψt ∈ L2 Q is taken as the control, and the solution to the obstacle problem is taken as the state. The goal is to find the optimal control so that the state is close to the desired profile while the norm of the obstacle is not too large. Existence and necessary conditions for the optimal control are established