A transmission problem for the reduced wave equation in inhomogeneous media with an infinite interface

Abstract

In this paper, we consider the transmission problem in R n ( n ≽ 2) for the reduced wave equation in inhomogeneous media with an infinite interface. A new radiation condition involving a surface integral over the interface, which is different from the well-known Rellich-Sommerfeld radiation condition, is introduced to ensure the uniqueness of the solutions. It is then used together with the limiting absorption principle to establish the unique existence of solutions to the problem in the various media.