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exponential term

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Optimal control of an ill-posed elliptic semilinear equation with an exponentialnon linearity
E. Casas, O. Kavian, J.-P. Puel
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 3 / 1998

Published online by Cambridge University Press:

15 August 2002, pp. 361-380

Print publication:

1998
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We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannotexpect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After havingdefined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of costfunctions using a non standard compactness argument. Then, we derive a first order optimality system assuming the optimal pair isslightly more regular.