Exterior dirichlet problem for the reduced wave equation: asymptotic analysis of low frequencies

Abstract

The order of convergence for the low frequency asymptotics of the exterior Dirichlet problem for the Helmholtz equation with variable, possibly non-smooth coefficients is shown to be Ω², the square of the frequency, except of some singular cases. In these cases the asymptotics are characterized completely by some lower order terms in the spherical harmonics expansion of the solution to the static problem.

Keywords:

• low frequency asymptotics
• reduced wave equation
• maximum principle
• exterior boundary value problems