Inverse boundary value problem for a linearized equations of longitudinal waves in rods

In this article, a question regarding the solvability of an inverse boundary value problem for the linearized equation of longitudinal waves in rods with an integral condition of the first kind was considered. For the considered inverse boundary value problem, the definition of a classical solution was introduced. Using the Fourier method, the problem was reduced to solving a system of integral equations. The method of contraction mappings is applied to prove the existence and uniqueness of a solution to the system of integral equations. The problem is to deduce the existence and uniqueness of the classical solution for the original problem.