Two-dimensional Inverse Boundary Value Problem for a Third-order Pseudo-hyperbolic Equation with an Additional Integral Condition

Abstract

In this paper we study an inverse boundary value problem with an unknown timedependent coefficient for a third-order pseudo-hyperbolic equation with an additional integral condition. The definition of the classical solution of the problem is given. 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. When solving the original inverse boundary value problem, the transition from the original inverse problem to some auxiliary inverse problem is carried out. The existence and uniqueness of a solution to an auxiliary problem are proved with the help of contracted mappings. Then the transition to the original inverse problem is again made, as a result, a conclusion is made about the solvability of the original inverse problem.