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An optimal control problem by parabolic equation with boundary smooth control and an integral constraint
Institute of Mathematics, Economics and Computer Science, Irkutsk State University, Irkutsk, Russia 
In the paper, we consider an optimal control problem by differential boundary condition of parabolic equation. We study this problem in the class of smooth controls satisfying certain integral constraints. For the problem under consideration we obtain a necessary optimality condition and propose a method for improving admissible controls. For illustration, we solve one numerical example to show the effectiveness of the proposed method.
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