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Zeitschrift für Analysis und ihre Anwendungen


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Volume 2, Issue 6, 1983, pp. 553–561
DOI: 10.4171/ZAA/84

Published online: 1983-12-31

Zur Existenz einer Lösung für ein bestimmtes parabolisches Randsteuerproblem

Wolfram Sperber[1]

(1) Brandenburgische Technische Universität Cottbus, Germany

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.

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Sperber Wolfram: Zur Existenz einer Lösung für ein bestimmtes parabolisches Randsteuerproblem. Z. Anal. Anwend. 2 (1983), 553-561. doi: 10.4171/ZAA/84