We study the 2-D Helmholtz equation in perturbed stratified media, allowing the existence of guided waves. Our assumptions on the perturbing and source terms are not too restrictive. We prove two results. Firstly, we introduce a Sommerfeld-Rellich radiation condition and prove the uniqueness of the solution for the studied equation. Then, by careful asymptotic estimates, we prove the existence of a bounded solution satisfying our radiation condition.
Ciraolo, G. (2009). A radiation condition for the 2-D Helmholtz equation in stratified media. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 34(12), 1592-1606 [10.1080/03605300903328075].
A radiation condition for the 2-D Helmholtz equation in stratified media
CIRAOLO, Giulio
2009-01-01
Abstract
We study the 2-D Helmholtz equation in perturbed stratified media, allowing the existence of guided waves. Our assumptions on the perturbing and source terms are not too restrictive. We prove two results. Firstly, we introduce a Sommerfeld-Rellich radiation condition and prove the uniqueness of the solution for the studied equation. Then, by careful asymptotic estimates, we prove the existence of a bounded solution satisfying our radiation condition.
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