A Radiation Condition for the 2-D Helmholtz Equation in Stratified Media

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.

Keywords:

• Green function
• Helmholtz equation
• Radiation condition

Mathematics Subject Classification:

• 35J05
• 78A40
• 78A50

Acknowledgments

The author thanks the anonymous referee for his helpful remarks and for suggesting reference [1].