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。
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 Helmhohz equation in a coaxi- al 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.
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
2014年第3期35-42,共8页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
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)
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
Helmhohz equation
coaxial waveguide
unbounded perturbation
existence of solutions
uniqueness of solutions
Green＇s function
radiation condition
