Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-10T15:14:45.405Z Has data issue: false hasContentIssue false
  • English
  • Français

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) 
Get access

Abstract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)