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RESEARCH PRODUCT

A radiation condition for the 2-D Helmholtz equation in stratified media

Giulio Ciraolo

subject

Helmholtz equationApplied MathematicsMathematical analysisEquazioni alle derivate parzialiSommerfeld radiation conditionRadiationMathematics - Analysis of PDEs35J05Bounded functionFOS: Mathematics35J05; 78A40UniquenessCondizione di radiazione78A40AnalysisAnalysis of PDEs (math.AP)Mathematics

description

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.

yearjournalcountryeditionlanguage
2009-01-01
http://arxiv.org/abs/0909.1662