A PROBLEM OF IDENTIFICATION OF A SPECIAL 2D MEMORY KERNEL IN AN INTEGRO–DIFFERENTIAL HYPERBOLIC EQUATION

We consider an inverse problem for a partial integro–differential equation of the second order related to recovering a kernel (memory) in the integral term of this equation. It is supposed that the unknown kernel is a trigonometric polynomial with respect to the spatial variables with coefficients continuous with respect to the time variable. The direct problem for a hyperbolic integro–differential equation is the initial-boundary value problem for the half-space x > 0 with the zero initial Cauchy data and a special Neumann data at x = 0. Local existence theorem and stability estimates for the solution to the inverse problem are obtained.