The problem of a point source of SH-waves in the case of separation of variables

Abstract

The equation

$$div(\mu \nabla u) + \omega ^2 \rho u = - \delta (x - x_0 )\delta (y - y_0 )$$

where μ(x, y)=α(x)β(y), ρ(x, y)=α(x)β(y)(g(x)+d(y)) (α, β, g, d are given step functions), is considered. The problem is solved in explicit form and the asymptotic expansion of the solutions as ω→+∞ is found.