INVERSE PROBLEM OF FINDING THE SOURCE FUNCTION IN THE WAVE PROPAGATION EQUATION

This article investigates an inverse problem of identifying the source function for a wave propagation equation. Initially, the mathematical formulation of the problem is presented, and the corresponding direct problem is solved using the Fourier method. Based on an additional condition, the existence, uniqueness, and stability of the solution to the inverse problem are analyzed. The research demonstrates that in certain instances, the inverse problem does not possess a unique solution and is ill-posed. Furthermore, theorems regarding the existence and estimation of the solution are proven. The results obtained are of significant importance for determining source functions in mathematical physics, signal processing, and various applied problems.