GLOBAL SOLVABILITY OF AN INVERSE PROBLEM FOR A MOORE-GIBSON-THOMPSON EQUATION WITH PERIODIC BOUNDARY AND INTEGRAL OVERDETERMINATION CONDITIONS

This article studies the inverse problem of determining the pressure and convolution kernel in an integro-differential Moore-Gibson-Thompson equation with initial, periodic boundary and integral overdetermination conditions on the rectangular domain. By Fourier method this problem is reduced to an equivalent integral equation and on based of Banach's fixed point argument in a suitably chosen function space, the local solvability of the problem is proven. Then, the found solutions are continued throughout the entire domain of definition of the unknowns.