Inverse problem for a second-order hyperbolic integro-differential equation with variable coefficients for lower derivatives

The problem of determining the memory of a medium from a second-order equation of hyperbolic type with a constant principal part and variable coefficients for lower derivatives is considered. The method is based on the reduction of the problem to a non-linear system of Volterra equations of the second kind and uses the fundamental solution constructed by S. L. Sobolev for hyperbolic equation with variable coefficients. The theorem of global uniqueness, stability and the local theorem of existence are proved.