中山大学学报自然科学版 ›› 2017, Vol. 56 ›› Issue (2): 36-39.

• 研究论文 • 上一篇    下一篇

全涂层的可穿透腔体散射问题的解的存在唯一性

刘立汉   

  1. 重庆师范大学数学科学学院, 重庆401331
  • 收稿日期:2016-08-11 出版日期:2017-03-25 发布日期:2017-03-25
  • 通讯作者: 刘立汉(1987年生),男;研究方向:数学物理方程的反问题;E-mail:mathsedu2013@163.com

The uniqueness and existence of solutions for the scattering problem for a fully coated penetrable cavity

LIU Lihan   

  1. School of Mathematial Sciences, Chongqing Normal University, Chongqing 401331, China
  • Received:2016-08-11 Online:2017-03-25 Published:2017-03-25

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。

关键词: 腔体, 散射, 解的存在性, 解的唯一性

Abstract:

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.

Key words: cavity, scattering, existence of solutions, uniqueness of solutions

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