Regional optimal control problem for a vibrating plate

In this paper, we examine the problem on the regional optimal control of a vibrating plate in a spatial domain $\Omega$. We obtain a bounded control that drives such a system from an initial state to a desired state in a finite time, only on a subdomain $\omega$ of $\Omega$. We prove that a regional optimal control exists characterize this control. Also we propose a condition that ensures the uniqueness of an optimal control and develop an algorithm for numerical simulations.