An Inverse Problem for a Hyperbolic Integro-DifferentialEquation in a Bounded Domain

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

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