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