MILD SOLUTIONS OF SEMILINEAR EVOLUTION INCLUSIONS AND OPTIMAL-CONTROL

In this paper we study semilinear evolution inclusions and their use i n optimal control problems. First we prove two existence theorems; one for convex valued orientor fields and the other for nonconvex valued ones. Then we establish a relaxation result showing that the mild solu tions of the nonconvex problem are dense in those of the convex proble m. We also consider a parametric version of the Cauchy problem and inv estigate how the solution set changes as the parameter varies. Subsequ ently, we turn our attention to feedback optimal control problems and study a time optimal control problem and the variational stability of a parameterized family of terminal cost problems. Some examples of par abolic systems are also included.