Boundary control problem for a parabolic equation with involution

In this paper, we consider a boundary control problem for a parabolic equation with involution in a bounded one-dimensional domain. On the part of the border of the considered domain, the value of the solution with control function is given. Restrictions on the control are given in such a way that the average value of the solution in the considered domain gets a given value. The problem given by the method of separation of variables is reduced to the Volterra integral equation of the first kind. The existence of the control function was proved by the Laplace transform method.

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