Boundary control associated with a parabolic equation

In this paper, we consider a boundary control problem associated with a parabolic equation. On the part of the border of the considered domain, the value of the solution with control parameter is given. Restrictions on the control are given in such a way that the average value of the solution in some part of the considered domain gets a given value. The auxiliary problem is solved by the method of separation of variables, while the problem in consideration is reduced to the Volterra integral equation. By Laplace transform method, the existence theorem for admissible control is proved.