The low frequency limit for time‐harmonic acoustic waves
Rainer H. Picard, Rolf Leis · Mathematical Methods in the Applied Sciences · 1986
Abstract The question of convergence of the solution of the exterior Dirichlet boundary value problem of the first order system of linearized acoustics as the frequency ω tends to zero is considered. The particular difficulty of having zero as an eigenvalue is handled by introducing certain scalar characteristics that — if prescribed — imply uniqueness in the limit case ω = 0. Convergence to the static solution in a weighted L2‐space is shown. Eventually the convergence result obtained can be extended to a larger class of boundary value problems of Mathematical Physics due to the structure of the argument.