Radiation principle for inhomogeneous media
Daniel Eidus · Journal of Mathematical Physics · 1998
The classical Sommerfeld radiation principle, well known for stationary oscillations in homogeneous media, is extended to a more general case where a smooth density ρ=ρ(x), x∈RN, depends both on r=|x| and on angular coordinates of the point x. We assume that the density behaves like a power rm, m>−2, at infinity, and, moreover, that there exists a one-parameter family of closed asymptotic wave fronts. A Sommerfeld–Rellich-type radiation condition is obtained and a corresponding theorem of unique solvability of the stationary oscillation problem is proved under some conditions imposed on the asymptotic phase. Some examples are given which include the case of elliptic wave fronts.