On solvability an inverse value problem for the equation of the third order describing the propagation of longitudinal waves in a dispersive medium with integral condition

The work is devoted to the study of the solvability of the inverse boundary value problem with an unknown time depended coefficient for the equation of the third order describing the propagation of longitudinal waves in a dispersive medium with integral condition. The problem is firstly reduced to the problem that is in a sense quivalent to the original. Then, the Fourier mathod is applied, reducing the problem to solution of a system of integral equations. The existence and uniqueness of the latter equation is proved by the contraction mapping principle, which also yoelds the unique solution of the equivalent problem. Using equivalence, we finally prove the unique existence of a classical solution of the problem under consideration.