Abstract
We consider a bilinear optimal control for an evolution equation involving the fractional Laplace operator of order 0<s<1. We first give some existence and uniqueness results for the considered evolution equation. Next, we establish some weak maximum principle results allowing us to obtain more regularity of our state equation. Then, we consider an optimal control problem which consists to bring the state of the system at final time to a desired state. We show that this optimal control problem has a solution and we derive the first- and second-order optimality conditions.
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