Problem of determining convolution kernel for hyperbolic integro - differential equation in bounded domain

We consider the inverse problem on determining the kernel of an integral term in an integro - differential equation. The problem of determining the memory kernel in the wave process is reduced to a nonlinear Volterra integral equation of the first kind of convolution type, then over determination condition it brings to the Volterra integral equation of the second kind. The method of contraction maps proves the unique solvability of the problem in the space of continuous functions with weight norms, and an estimate of the conditional stability of the solution is obtained.