Inverse Problem for Moore-Gibson-Thompson equation with integral overdetermination condition

This article is dedicated to the solution of the initial-boundary value problem for the Moore-Gibson-Thompson equation and introduces the inverse problem of identifying the kernel using an additional integral condition. First, we prove the existence and uniqueness of the solution to the direct problem and provide a priori estimates for it. Then we consider a new problem that is equivalent to the direct problem, and we use it to investigate the inverse problem. By applying a fixed point theorem in a suitable Sobolev space, we obtain global existence and uniqueness results for the inverse problem.