Analysis and semidiscrete galerkin approximation of A class of nonlinear hyperbolic optimal control problems

This paper presents an optimization problem involving a system governed by a nonlinear hyperbolic equation with control acting on the domain, in the boundary conditions, or in the initial conditions. The quadratic cost function is the classical one. We present the Galerkin approximation and we demonstrate existence of the weak and strong condensation points of a set of solutions of the approximate optimization problems. Each of these points is a solution of the initial optimization problem