Inverse Problem for an Integro-Differential Wave Equation in a Cylindrical Domain

In this paper, for an integro-differential wave equation in a cylindrical domain it is studied an inverse problem of searching the unknown kernel in the integral term. By the method of separation of variables, the problem is reduced to determine the same kernel from ordinary differential equations with respect to coefficients of Fourier-Bessel series of the solution of the direct problem. Orthonormal Bessel functions of the first kind of zero order is used. An additional information obtained in the form of Volterra integral equation of the second is used. It is proved the global unique solvability of the inverse problem by the method of contraction mappings in the space of continuous functions with weighted norms.