Analogues of the Cauchy-Goursat problem for a loaded third-order hyperbolic type equation in an infinite three-dimensional domain

Abstract

In this article it is studied the analogue of Cauchy-Goursat problem for a loaded third-order hyperbolic type differential equation in an infinite three-dimensional domain. The main research method is the Fourier transform of studying the analogous of the Cauchy-Goursat problem. Based on this Fourier transform, the given problem reduces to a flat analogue of the Cauchy-Goursat problem with a spectral parameter with boundary value conditions. The asymptotic behavior of the solution of plane analogues of the Cauchy-Goursat problem for large values of the spectral parameter is studied. Sufficient conditions are obtained, according to which all operations in this paper are legal.