Matrix Fourier transform in dynamic theory of elasticity of piecewise homogeneous medium

Abstract

The analytical solving dynamic problems of elasticity theory for piecewise homogeneous half-space is found. The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of mathematical physics in the heterogeneous environments is developed on an example of the dynamic problems of the elasticity theory.