On an Inverse Boundary Value Problem with Non-Local on Time Conditions for a Fourth Order Pseudo Parabolic Equation

In this paper, we study an inverse boundary value problem with unknown time depend coefficients for fourth-order pseudoparabolic equations with a nonlocal integral conditions of the second kind. The essence of the problem is that it is required, together with the solution, to determine the unknown coefficient. The problem is considered in a rectangular area. Solving the initial inverse boundary value problem, a transition is made from the original inverse problem to some auxiliary inverse problem. Using compressed mappings, the existence and uniqueness of the solution of the auxiliary problem is proved. In the conclusion we obtained the solvability of the original inverse problem.