Abstract.

An inverse boundary value problem for a two-dimensional linearized equation de scribing longitudinal waves in rods with an additional integral condition is studied. First, the original problem is reduced to an equivalent problem. Using the Fourier method, the equivalent problem is reduced to a system of integral equations. By means of the contraction mapping method, we prove the existence and uniqueness of a solution to the system of integral equa tions, which, in turn, is the unique solution of the equivalent problem. By the equivalence, the existence and uniqueness of a classical solution to the original problem are established.

Keywords:

inverse, boundary value problem, two-dimensional linearized equation, longitudinal waves, rods, Fourier method, classic solution.