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 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.
Lingua originaleEnglish
pagine (da-a)1592-1606
Numero di pagine15
RivistaCommunications in Partial Differential Equations
Volume34
Stato di pubblicazionePublished - 2009

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Radiation Condition
Helmholtz equation
Guided electromagnetic wave propagation
Helmholtz Equation
Radiation
Guided Waves
Asymptotic Estimates
Bounded Solutions
Source Terms
Uniqueness

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cita questo

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title = "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 = "Equazioni alle derivate parziali; Condizione di radiazione",
author = "Giulio Ciraolo",
year = "2009",
language = "English",
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journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
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T1 - A radiation condition for the 2-D Helmholtz equation in stratified media

AU - Ciraolo, Giulio

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Equazioni alle derivate parziali; Condizione di radiazione

UR - http://hdl.handle.net/10447/40028

M3 - Article

VL - 34

SP - 1592

EP - 1606

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

SN - 0360-5302

ER -