On the Control Problem for a Heat Conduction Equation with Involution in a Two-Dimensional Domain

In this article, we consider a boundary control problem for a heat conduction equation with involution in a two-dimensional domain. On the part of the border of the considered domain, the value of the solution with control function is given. Restriction on the control function is given in such a way that the average of 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 is proved by the Laplace transform method.

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