A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equation

The inverse problem of determining 2D spatial part of integral member kernel in integro‐differential wave equation is considered. It is supposed that the unknown function is a trigonometric polynomial with respect to the spatial variable y with coefficients continuous with respect to the variable x. Herein, the direct problem is represented by the initial‐boundary value problem for the half‐space x>0 with the zero initial Cauchy data and Neumann boundary condition as Dirac delta function concentrated on the boundary of the domain . Local existence and uniqueness theorem for the solution to the inverse problem is obtained.