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On the variational stability of a class of nonlinear parabolic optimal control problems

Published online by Cambridge University Press:  17 February 2009

Nikolaos S. Papageorgiou
Nikolaos S. Papageorgiou
Affiliation:
National Technical University, Department of Mathematics, Zografou Campus, Athens 15780, GREECE
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Abstract

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In this paper we study parametric optimal control problems governed by a nonlinear parabolic equation in divergence form. The parameter appears in all the data of the problem, including the partial differential operator. Using as tools the G-convergence of operators and the Γ-convergence of functionals, we show that the set-valued map of optimal pairs is upper semicontinuous with respect to the parameter and the optimal value function responds continuously to changes of the parameter. Finally in the case of semilinear systems we show that our framework can also incorporate systems with weakly convergent coefficients.

Type
Research Article
Information
The ANZIAM Journal , Volume 39 , Issue 1 , July 1997 , pp. 77 - 92
Copyright
Copyright © Australian Mathematical Society 1997

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