Global solvability of two unknown variables identification problem in one inverse problem for the integro-differential wave equation

Abstract

Identification problem of the two coefficients, one of which is located under the integral sign in a hyperbolic equation and represents memory of the medium is studied, the other one defines a regular part of an impulse source. As an additional information Fourier image of the solution's trace of a direct problem on the hyperplane y=0 for two different values of transformation parameters is applied. The global solvability and the estimate of stability of the inverse problem are defined.