The Goursat problem for a system of hyperbolic-type equations

Abstract

In this paper, the well-posed Goursat-type problem for a system of hyperbolic equations is studied. The mathematical model of the problem is analyzed, and the existence and uniqueness of the solution, as well as its dependence on the given initial and boundary conditions, are investigated. In addition, the properties of the system of hyperbolic equations and their possibilities for practical applications are analyzed. The obtained results are of significant importance in mathematical physics, wave processes, and the modeling of dynamic phenomena in elastic media.