An Optimal Control Problem for a Parabolic Equation in the Class of Smooth Controls

We consider an optimal control problem for a parabolic equation with a differential constraint on the boundary. We study this problem in the class of smooth controls satisfying certain pointwise constraints. Such problems describe mass transfer processes in column-type apparatuses, taking into account the longitudinal mixing. Control functions in these problems represent flows of raw materials or finished products. For the problem under consideration we obtain a necessary optimality condition, propose a method for improving admissible controls, and carry out the numerical experiment.