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

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Abstract

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.
Original languageEnglish
Pages (from-to)1592-1606
Number of pages15
JournalCommunications in Partial Differential Equations
Volume34
Publication statusPublished - 2009

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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