发表状态 | 已发表Published |
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
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ISSN/eISSN | 0266-5611 |
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 |
DOI | 10.1088/1361-6420/aa8826 |
URL | 查看来源 |
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 | |
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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