On Green's functions for the reduced wave equation in a circular annular domain with dirichlet, Neumann and radiation type boundary conditions

Abstract

In this paper Green's functions for the reduced wave equation (Helmholtz equation) in a circular annular domain with the Dirichlet, the radiation, and Neumann boundary conditions are derived. The convergence of the series representing Green's functions is then established. Finally it is shown that these functions reduce to Green's function for the exterior of a circle as given by Franz and Etienne when the outer radius is moved towards infinity.