​THE INVERSE PROBLEM OF DETERMINING THE COEFFICIENT FOR THE WAVE PROPAGATION EQUATION

Abstract

 This article investigates an inverse problem of determining unknown coefficients in wave propagation processes described by second-order hyperbolic partial differential equations. The relevance of the study is обусловлено the need to analyze wave dynamics in heterogeneous media and to determine the internal characteristics of a medium through remote measurements. The paper theoretically examines the conditions of well-posedness of the problem, in particular the existence, uniqueness, and stability of the solution in the sense of Hadamard. Additional data obtained at boundary or internal points are used to identify the unknown coefficient. Iterative methods based on solving nonlinear operator equations are proposed, and the efficiency of the suggested algorithms is demonstrated through numerical simulations. The obtained results have important practical applications in fields such as seismic exploration, hydroacoustics, and medical tomography.