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

E. Casas; O. Kavian; J.-P. Puel

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 3, page 361-380
- ISSN: 1292-8119

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topCasas, 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 -

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