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.
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 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.",
keywords = "Condizione di radiazione, Equazioni alle derivate parziali",
author = "Giulio Ciraolo",
year = "2009",
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journal = "Communications in Partial Differential Equations",
issn = "0360-5302",
publisher = "Taylor and Francis Ltd.",

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TY - JOUR

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 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.

AB - 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.

KW - Condizione di radiazione

KW - Equazioni alle derivate parziali

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 -