On the Solvability of a Time Nonlocal Inverse Coefficient Problem for the Equation of Longitudinal Wave Propagation

This paper investigates the classical solvability of the inverse problem for an equation of longitudinal wave propagation with nonlocal boundary conditions. In this context, the original problem is reduced to an auxiliary problem and the equivalence of the auxiliary problem to the considered one is proved. Then, by means of the Fourier method the auxiliary problem is presented as a system of integral equations. Further, using the contraction mappings principle the existence and uniqueness of the solution of the obtained system of integral equations is shown. Based on the equivalence of the problems, a theorem on the unique existence of the classical solution to the original inverse boundary value problem is proved.