DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

doi:10.1016/S0252-9602(17)30120-0

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 110-124.doi: 10.1016/S0252-9602(17)30120-0

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

孙美满¹, 严国政^1,2

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Hubei Key Laboratory of Mathematical Physics, Wuhan 430079, China

收稿日期:2016-12-12 出版日期:2018-02-25 发布日期:2018-02-25
通讯作者: Guozheng YAN E-mail:yan_gz@mail.ccnu.edu.cn
作者简介:Meiman SUN,E-mail:534031902@qq.com
基金资助:
This research is supported by National Natural Science Foundation of People's Republic of China (11571132 and 11171127), and Supported in Part by Program for Changjiang Scholars and Innovative Research Team in University No.IRT13066.

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

Meiman SUN¹, Guozheng YAN^1,2

1. School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
2. Hubei Key Laboratory of Mathematical Physics, Wuhan 430079, China

Received:2016-12-12 Online:2018-02-25 Published:2018-02-25
Contact: Guozheng YAN E-mail:yan_gz@mail.ccnu.edu.cn
Supported by:
This research is supported by National Natural Science Foundation of People's Republic of China (11571132 and 11171127), and Supported in Part by Program for Changjiang Scholars and Innovative Research Team in University No.IRT13066.

摘要/Abstract

摘要：

In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.

关键词: exterior transmission eigenvalue, inverse scattering problem, Helmholtz equation

Abstract:

Key words: exterior transmission eigenvalue, inverse scattering problem, Helmholtz equation

孙美满, 严国政. DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES[J]. 数学物理学报(英文版), 2018, 38(1): 110-124.

Meiman SUN, Guozheng YAN. DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES[J]. Acta mathematica scientia,Series B, 2018, 38(1): 110-124.

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DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

DISCRETENESS OF THE EXTERIOR TRANSMISSION EIGENVALUES

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