On the Control Problem Associated With a Pseudo-Parabolic Type Equation in an One-Dimensional Domain

In previous works, the control problem for the initial-boundary value problem in the interval for such a pseudo-parabolic type equation was studied.That is, the Dirichlet boundary value problem was considered.In this work we consider control problem for a homogeneous pseudo-parabolic type equation.In the part of the bound of the given region it is given value of the derivative of the solution with the respect to the normal and it is required to find control to get the average value of solution.By the Laplace transform method it is proved that like this control exists.