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

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.