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Optimal control of an ill-posed elliptic semilinear equation with an exponentialnon linearity

Published online by Cambridge University Press:  15 August 2002

E. Casas ,
O. Kavian  and
J.-P. Puel
E. Casas
Affiliation:
(casas@etsiso.macc.unican.es)
O. Kavian
Affiliation:
(kavian@math.uvsq.fr) 
J.-P. Puel
Affiliation:
(jppuel@cmapx.polytechnique.fr) 
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Abstract

We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality system assuming the optimal pair is slightly more regular.

Keywords

Optimal controlsemilinear equationexponential termoptimality conditions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 3 , 1998 , pp. 361 - 380
Copyright
© EDP Sciences, SMAI, 1998

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