We study the 2-D Helmholtz equation in perturbed stratified media,allowing the existence of guided waves. Our assumptions on theperturbing and source terms are not too restrictive.We prove two results. Firstly, we introduce a Sommerfeld-Rellichradiation condition and prove the uniqueness of the solution for thestudied equation. Then, by careful asymptotic estimates, we provethe existence of a bounded solution satisfying our radiationcondition.
|Number of pages||15|
|Journal||Communications in Partial Differential Equations|
|Publication status||Published - 2009|
All Science Journal Classification (ASJC) codes
- Applied Mathematics