We consider an optimal control problem where the state satisfies an obstacle type semilinear variational inequality and the control function is the obstacle. The state is chosen to be close to a desired profile while the obstacle is not too large in H1, and H2-bounded. We prove that an optimal control exists and give necessary optimality conditions, using approximation techniques.
Publié le : 2004-07-05
Classification:
Optimal control,
obstacle problem,
variational inequalities,
semilinear elliptic equations,
AMS 49J20,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00022012,
author = {Bergounioux, Ma\"\i tine and Lenhart, Suzanne, },
title = {Optimal control of the obstacle in semilinear variational inequalities},
journal = {HAL},
volume = {2004},
number = {0},
year = {2004},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00022012}
}
Bergounioux, Maïtine; Lenhart, Suzanne, . Optimal control of the obstacle in semilinear variational inequalities. HAL, Tome 2004 (2004) no. 0, . http://gdmltest.u-ga.fr/item/hal-00022012/