The uniqueness and existence of solutions for the 3-D Helmholtz equation in a stratified medium with unbounded perturbation

摘要

In this paper, we study the 3D Helmholtz equation in perturbed stratified media, allowing the presence of guided waves. Our assumptions on the perturbed and source terms are too few. On the basis of the knowledge of the Green's function for the 3D homogeneous Helmholtz equation in unperturbed stratified media, we introduce a generalized (out-going) Sommerfeld-Rellich radiation condition, and then we prove the uniqueness and existence of solutions for the studied 3D Helmholtz equation satisfying our radiation condition.