| 三维Helmholtz方程在扰动的共轴波导上的解的存在唯一性 |
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| 引用本文： | 刘立汉. 三维Helmholtz方程在扰动的共轴波导上的解的存在唯一性[J]. 中山大学学报(自然科学版), 2014, 53(3): 35-42 |
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| 作者姓名： | 刘立汉 |
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| 作者单位： | 重庆师范大学数学学院, 重庆401331 |
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| 基金项目： | 2013年重庆高校创新团队建设计划资助项目(KJTD201308);重庆师范大学基金项目资助项目(13XLB015) |
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| 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。
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| 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 |
| 收稿时间： | 2013-09-16; |
The Uniqueness and Existence of Solutions for the 3-D Helmholtz Equation in a Coaxial Waveguide with Unbounded Perturbation |
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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, 2014, 53(3): 35-42 |
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| Authors: | LIU Lihan |
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| Affiliation: | School of Mathematics, Chongqing Normal University, Chongqing 401331, China |
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| 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. |
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| Keywords: | Helmholtz equation coaxial waveguide unbounded perturbation existence of solutions uniqueness of solutions Green's function radiation condition |
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