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题名On vanishing and localizing of transmission eigenfunctions near singular points: A numerical study
作者
发表日期2017-09-07
发表期刊Inverse Problems
ISSN/eISSN0266-5611
卷号33期号:10
摘要

This paper is concerned with the intrinsic geometric structure of interior transmission eigenfunctions arising in wave scattering theory. We numerically show that the aforementioned geometric structure can be very delicate and intriguing. The major findings can be roughly summarized as follows. We say that a point on the boundary of the inhomogeneity is singular if the surface tangent is discontinuous there. The interior transmission eigenfunction then vanishes near a singular point where the interior angle is less than π, whereas the interior transmission eigenfunction localizes near a singular point if its interior angle is bigger than π. Furthermore, we show that the vanishing and blowup orders are inversely proportional to the interior angle of the singular point: the sharper the corner, the higher the convergence order. Our results are first of its type in the spectral theory for transmission eigenvalue problems, and the existing studies in the literature concentrate more on the intrinsic properties of the transmission eigenvalues instead of the transmission eigenfunctions. Due to the finiteness of computing resources, our study is by no means exclusive and complete. We consider our study only in a certain geometric setup including corner, curved corner and edge singularities. Nevertheless, we believe that similar results hold for more general singularities and rigorous theoretical justifications are much desirable. Our study enriches the spectral theory for transmission eigenvalue problems. We also discuss its implication to inverse scattering theory.

关键词acoustic scattering corner singularity inverse scattering spetral theory transmission eigenfunction vanishing and localizing
DOI10.1088/1361-6420/aa8826
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收录类别SCIE
语种英语English
WOS研究方向Mathematics ; Physics
WOS类目Mathematics, Applied ; Physics, Mathematical
WOS记录号WOS:000410094300001
Scopus入藏号2-s2.0-85029842601
引用统计
被引频次:33[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符https://repository.uic.edu.cn/handle/39GCC9TT/7950
专题个人在本单位外知识产出
理工科技学院
通讯作者Liu, Hongyu
作者单位
1.HKUST Jockey Club Institute for Advanced Study,Hong Kong University of Science and Technology,Hong Kong
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
3.Department of Mathematics,Hong Kong Baptist University,Kowloon Tong,Hong Kong
4.HKBU Institute of Research and Continuing Education,Virtual University Park,Shenzhen,China
推荐引用方式
GB/T 7714
Blasten, Eemeli,Li, Xiaofei,Liu, Hongyuet al. On vanishing and localizing of transmission eigenfunctions near singular points: A numerical study[J]. Inverse Problems, 2017, 33(10).
APA Blasten, Eemeli, Li, Xiaofei, Liu, Hongyu, & Wang, Yuliang. (2017). On vanishing and localizing of transmission eigenfunctions near singular points: A numerical study. Inverse Problems, 33(10).
MLA Blasten, Eemeli,et al."On vanishing and localizing of transmission eigenfunctions near singular points: A numerical study". Inverse Problems 33.10(2017).
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