Zur Existenz einer Lösung für ein bestimmtes parabolisches Randsteuerproblem

  • Wolfram Sperber

    Brandenburgische Technische Universität Cottbus, Germany

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.

Cite this article

Wolfram Sperber, Zur Existenz einer Lösung für ein bestimmtes parabolisches Randsteuerproblem. Z. Anal. Anwend. 2 (1983), no. 6, pp. 553–561

DOI 10.4171/ZAA/84