APPROXIMATION OF RELAXED NONLINEAR PARABOLIC OPTIMAL-CONTROL PROBLEMS

We consider a relaxed optimal control problem for systems defined by n onlinear parabolic partial differential equations with distributed con trol. The problem is completely discretized by using a finite-element approximation scheme with piecewise linear states and piecewise consta nt controls. Existence of optimal controls and necessary conditions fo r optimality are derived for both the continuous and the discrete prob lem. We then prove that accumulation points of sequences of discrete o ptimal [resp. extremal] controls are optimal [resp. extremal] for the continuous problem.