# Boundary control for pseudoparabolic equations in space

### Abstract

Let $u(x, y, t)$ be a solution to the pseudoparabolic equation that satisfies the initial and boundary conditions. The value of the solution is given on the part of boundary of the considered region which contains the control parameter. It is required to choose the control parameter so that on a part of the regularity domain the solution takes the specified mean value. First, we consider an auxiliary boundary value problem for a pseudoparabolic equation. We prove the existence and uniqueness of the generalized solution from the corresponding class. The restriction for the admissible control is given in the integral form. By the separation variables method, the desired problem is reduced to the Volterra integral equation. The latter is solved by the Laplace transform method. The theorem on the existence of an admissible control is proved.

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*Mathematical notes of NEFU*, 26(3), pp. 98-108. doi: https://doi.org/10.25587/SVFU.2019.20.57.008.

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