Finding the Two-Dimensional Relaxation Kernel of an Integro-Differential Wave Equation

Abstract

We consider the multidimensional inverse problem of determining the kernel of the integral term in an integro-differential wave equation. In the direct problem, it is required to find the displacement function from an initial–boundary value problem, and in the inverse one, to determine the kernel of the integral term depending on both time and one of the spatial variables. The local unique solvability of the problem in the class of functions continuous in one of the variables and analytic in the other one is proved on the basis of the method of scales of Banach spaces of real analytic functions.