论文信息 - Optimal Control of Bilateral Obstacle Problems

Optimal Control of Bilateral Obstacle Problems

We consider an optimal control problem where the state satisfies a bilateral elliptic variational inequality and the control functions are the upper and lower obstacles. We seek a state that is close to a desired profile and the H2 norms of the obstacles are not too large. Existence results are given and an optimality system is derived. A particular case is studied that needs no compactness assumption, via a monotonicity method.

Maïtine Bergounioux | Suzanne M. Lenhart | M. Bergounioux | S. Lenhart

[1] P. Bassanini,et al. Elliptic Partial Differential Equations of Second Order , 1997 .

[2] Suzanne Lenhart,et al. Optimal Control of the Obstacle for an Elliptic Variational Inequality , 1998 .

[3] Suzanne Lenhart,et al. An Obstacle Control Problem with a Source Term , 2002 .

[4] M. Chipot. Variational Inequalities and Flow in Porous Media , 1984 .

[5] J. Lions,et al. Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles , 1968 .

[6] Suzanne Lenhart,et al. Optimal Control of the Obstacle for a Parabolic Variational Inequality , 2002 .

[7] Suzanne Lenhart,et al. Optimal control of the obstacle in semilinear variational inequalities , 2004 .

[8] Hongwei Lou,et al. On the Regularity of an Obstacle Control Problem , 2001 .

[9] Qihong Chen. Optimal Control of Semilinear Elliptic Variational Bilateral Problem , 2000 .

[10] Maïtine Bergounioux. Optimal Control of Semilinear Elliptic Obstacle Problems , 2002 .