Regularized Optimal Design Problem for a Viscoelastic Plate Vibrating Against a Rigid Obstacle

Abstract

We deal with a regularized optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing behaviour of a viscoelastic plate vibrating against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. The original problem for the deflection is regularized in order to have the uniqueness of a solution to the state problem and only the existence of an optimal thickness but also necessary optimality conditions.