I. Sigua and Z. Tediashvili

On Fundamental Solution of Steady State Oscillation Equations

abstract:
The system of differential equations of steady state oscillations of anisotropic elasticity are considered. By the generalized Fourier transform technique and with the help of the limiting absorbtion principle, we construct maximally decaying at infinity matrices of fundamental solutions explicitly. Their expressions contain surface integral over a certain semi-sphere and a line integral along the edge boundary of the semi-sphere. We investigate near field and far field properties of the fundamental matrices and show that they satisfy the generalized Sommerfeld-Kupradze type radiation conditions at infinity.

Mathematics Subject Classification: 35J15, 74B05, 74J05

Key words and phrases: Elliptic systems, fundamental solution, steady state oscillations