Inverse boundary value problem for a second-order hyperbolic equation with integral condition of the first kind

An inverse boundary value problem for a second-order hyperbolic equation with integral condition of the first kind is investigated. A definition of classical solution is introduced for this problem. The Fourier method is used to reduce the problem to a system of integral equations. The method of contraction mappings is applied to prove the existence and uniqueness of a solution of the system of integral equations. Then, the existence and uniqueness of a classical solution of the initial problem is proved.