On one boundary control problem for a pseudo-parabolic equation in a two-dimensional domain

In this paper, we consider a boundary control problem associated with a non-homogeneous pseudo-parabolic type equation in a bounded two-dimensional domain. In the part of the bound of the given region, the value of the solution is given, and it is required to find control to get the average value of the solution. The initial-boundary problem is solved by the Fourier method, and the control problem under consideration is analyzed with the Volterra integral equation of the second kind. The control function is found using the Laplace transform method and proved to be admissible.