An Inverse Problem for Determining Two Coefficients in an Integrodifferential Wave Equation

For the equation of wave propagation in the half-space filled with some medium, we consider the problem of determining the wave propagation velocity which depends only on the variable $y$ and the memory functions of the medium. There is a point-like pulse source on the boundary of the half-space. We show that both unknown functions of one variable are uniquely determined by the Fourier image with respect to $x$ of the solution to the direct problem on the boundary of the half-space. We estimate the stability of the solution to the problem.