An Inverse Problem for a Hyperbolic Integro-Differential Equation in a Bounded Domain

We consider the inverse problem of finding the kernel of the integral term in anintegro-differential equation. The problem of finding the memory kernel in the wave process isreduced to a nonlinear Volterra integral equation of the first kind of convolution type, which is inturn reduced under some assumptions to a Volterra integral equation of the second kind. Usingthe method of contraction mappings, we prove the unique solvability of the problem in the spaceof continuous functions with weighted norms and obtain an estimate of the conditional stability ofthe solution.