The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation

LIU Lihan

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The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation

更新时间：2023-12-11

- The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 53, Issue 3, Pages: 35-42(2014)
- 作者机构：
  
  重庆师范大学数学学院,重庆,401331
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2014，
  
  Published Online：25 May 2014，
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LIU Lihan. The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):35-42(2014)
DOI：

LIU Lihan. The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 53(3):35-42(2014) DOI：

摘要

在允许导波存在的情况下，研究了三维Helmholtz方程在扰动的共轴波导上的解的存在唯一性。对扰动项和点源项的假设要求很少。首先，在知道三维齐次Helmholtz方程在无扰动的共轴波导的Green函数的基础上，引进了一个推广的Sommerfeld-Rellich辐射条件(输出辐射条件)。然后，证明了满足给定的辐射条件的三维Helmholtz方程在扰动的共轴波导上的解的存在性及唯一性。

Abstract

The 3-D Helmholtz equation in a coaxial waveguide with unbounded perturbation is studied

allowing the presence of guided waves

while a few assumptions on the perturbation and the source term are adapted. On the basis of the Green's function for the 3-D homogeneous Helmholtz equation in a coaxial waveguide without perturbation

a generalized (out-going) Sommerfeld-Rellich radiation condition is introduced. And then the uniqueness and existence of solutions for the studied 3-D Helmholtz equation satisfying some radiation conditions are proven.

关键词

Helmholtz方程共轴波导扰动解的存在性解的唯一性Green函数辐射条件

Keywords

Helmholtz equationcoaxial waveguideunbounded perturbationexistence of solutionsuniqueness of solutionsGreen's functionradiation condition

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Related Author

LIU Lihan

黄民海

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Related Institution

School of Mathematial Sciences, Chongqing Normal University

School of Mathematics and Computational Science, Sun Yatsen University

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