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 H 0 1 (Ω), and H 2-bounded. We prove that an optimal control exists and give necessary optimality conditions, using approximation techniques.
Positivity – Springer Journals
Published: Dec 30, 2004
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