On the problem of identifying a linear source for the third-order hyperbolic equation with integral condition

The identification of a linear source for the third-order single equation that describes the propagation of longitudinal waves in a dispersive medium with an integral condition of the first kind is investigated. At first, the original problem reduces to an equivalent problem in a certain sense. Using the Fourier method, the equivalent problem is reduced to solving a system of integral equations. With the help of the method of compressed mappings, the existence and uniqueness of the solution of a system of integral equations, which is also the only solution to an equivalent problem, are proved. Using equivalence, it is possible to prove the existence and uniqueness of the classical solution of the original problem.