摘要
利用变分法研究了全涂层的可穿透腔体散射问题的解的存在唯一性。首先,应用Green公式把微分方程转化为积分方程后,由Rellich引理和唯一延拓原理,证明了全涂层的可穿透腔体散射问题的解的唯一性。然后,由Dirichlet-to-Neumann算子理论、迹定理、连续嵌入定理和Lax-Milgram引理,证明了全涂层的可穿透腔体散射问题的解的存在性。
The uniqueness and existence of solutions for the scattering problem for a fully coated penetrable cavity are studied by using variational method. First,the differential equations are transformed into an integral equation by using the Green＇s first identity. Then from the Rellich＇s lemma and a unique continuation principle,the uniqueness of solutions for the scattering problem for a fully coated penetrable cavity is proven. Next,from the Dirichlet-to-Neumann operator,the trace theorem,the continuous embedding theorem and the Lax-Milgram＇s lemma,the existence of solutions for the scattering problem for a fully coated penetrable cavity is also proven.
作者
刘立汉
LIU Lihan(School of Mathematial Sciences, Chongqing Normal University, Chongqing 401331, China)
出处
《中山大学学报（自然科学版）》
CAS
CSCD
北大核心
2017年第2期36-39,共4页
Acta Scientiarum Naturalium Universitatis Sunyatseni
基金
国家自然科学基金数学天元青年基金(11426052)
重庆市教育委员会科学技术研究项目(KJ1400522
KJ1600329)
2013年重庆高校创新团队建设计划项目(KJTD201308)
关键词
腔体
散射
解的存在性
解的唯一性
cavity
scattering
existence of solutions
uniqueness of solutions
