KMS Of Academy of mathematics and systems sciences, CAS
| A NOTE ON TRANSMISSION EIGENVALUES IN | |
Cakoni, Fioralba1; Meng, Shixu2 ; Xiao, Jingni1
| |
| 2021-10-01 | |
| 发表期刊 | INVERSE PROBLEMS AND IMAGING
 |
| ISSN | 1930-8337 |
| 卷号 | 15期号:5页码:999-1014 |
| 摘要 | This short note was motivated by our efforts to investigate whether there exists a half plane free of transmission eigenvalues for Maxwell's equations. This question is related to solvability of the time domain interior transmission problem which plays a fundamental role in the justification of linear sampling and factorization methods with time dependent data. Our original goal was to adapt semiclassical analysis techniques developed in [21, 23] to prove that for some combination of electromagnetic parameters, the transmission eigenvalues lie in a strip around the real axis. Unfortunately we failed. To try to understand why, we looked at the particular example of spherically symmetric media, which provided us with some insight on why we couldn't prove the above result. Hence this paper reports our findings on the location of all transmission eigenvalues and the existence of complex transmission eigenvalues for Maxwell's equations for spherically stratified media. We hope that these results can provide reasonable conjectures for general electromagnetic media. |
| 关键词 | Key words and phrases Inverse problems Maxwell equations transmission eigenvalues scat-tering theory distribution of eigenvalues |
| DOI | 10.3934/ipi.2021025 |
| 收录类别 | SCI |
| 语种 | 英语 |
| 资助项目 | AFOSR[FA9550-20-1-0024] ; NSF[DMS-1813492] |
| WOS研究方向 | Mathematics ; Physics |
| WOS类目 | Mathematics, Applied ; Physics, Mathematical |
| WOS记录号 | WOS:000683552600008 |
| 出版者 | AMER INST MATHEMATICAL SCIENCES-AIMS |
| 引用统计 | |
| 文献类型 | 期刊论文 |
| 条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/59117 |
| 专题 | 应用数学研究所 |
| 通讯作者 | Xiao, Jingni |
| 作者单位 | 1.Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA 2.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Cakoni, Fioralba,Meng, Shixu,Xiao, Jingni. A NOTE ON TRANSMISSION EIGENVALUES IN[J]. INVERSE PROBLEMS AND IMAGING,2021,15(5):999-1014. |
| APA | Cakoni, Fioralba,Meng, Shixu,&Xiao, Jingni.(2021).A NOTE ON TRANSMISSION EIGENVALUES IN.INVERSE PROBLEMS AND IMAGING,15(5),999-1014. |
| MLA | Cakoni, Fioralba,et al."A NOTE ON TRANSMISSION EIGENVALUES IN".INVERSE PROBLEMS AND IMAGING 15.5(2021):999-1014. |
| 条目包含的文件 | 条目无相关文件。 | |||||
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。
修改评论