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

Casas, E., Kavian, O., and Puel, J.-P.. "Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity ." ESAIM: Control, Optimisation and Calculus of Variations 3 (2010): 361-380. <http://eudml.org/doc/197284>.

@article{Casas2010,
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. },
author = {Casas, E., Kavian, O., Puel, J.-P.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Optimal control; semilinear equation; exponential term; optimality conditions. ; elliptic equation; exponential nonlinearity; existence of solutions; optimal control; necessary optimality conditions},
language = {eng},
month = {3},
pages = {361-380},
publisher = {EDP Sciences},
title = {Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity },
url = {http://eudml.org/doc/197284},
volume = {3},
year = {2010},
}

TY - JOUR
AU - Casas, E.
AU - Kavian, O.
AU - Puel, J.-P.
TI - Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 3
SP - 361
EP - 380
AB - 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.
LA - eng
KW - Optimal control; semilinear equation; exponential term; optimality conditions. ; elliptic equation; exponential nonlinearity; existence of solutions; optimal control; necessary optimality conditions
UR - http://eudml.org/doc/197284
ER -