BOUNDARY CONTROL PROBLEM ASSOCIATED WITH A PSEUDO-PARABOLIC EQUATION

Previously, boundary control problems for a parabolic type equations were considered.A portion of the thin rod boundary has a temperaturecontrolled heater.Its mode of operation should be found so that the average temperature in some region reaches a certain value.In this paper, we consider the boundary control problem for a pseudo-parabolic equation in a right rectangle domain.The value of the solution with the control parameter is given in the boundary of the domain.Control constraints are given such that the average value of the solution in considered domain takes a given value.The auxiliary problem is solved by the method of separation of variables, and the problem under consideration is reduced to the Volterra integral equation.The existence theorem of admissible control is proved by the Laplace transform method.

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