Infinite Dimensional Par~metric Optimal Control Problems 1

In this paper we study parametric optimal control problems monitored by nonlinear evolution equations. The parameter appears in all the data, including the nonlinear operator. First we show that for every value of the parameter, the optimal control problem has a solution. Then we study how these solutions as well as the value of the problem respond to changes in the parazneter. Finally, we work out in detail two examples of nonlinear parabolic optimal control systems.