Zur Existenz einer Lösung für ein bestimmtes parabolisches Randsteuerproblem

Abstract

This paper investigates the existence of an optimal control for a control problem with a parabolic state equation. The state equation of the boundary control problem is a weakly nonlinear parabolic third initial boundary value problem. For this problem a generalized solution is defined by means of the integral equation method. The existence of a solution is proved by an approximation using solutions of classically solvable problems. To show the existence of an optimal control a generalization of the theorem of Weierstrass to lower semi-continuous functionals on reflexive Banach spaces is used.