A NOTE ON TRANSMISSION EIGENVALUES IN

doi:10.3934/ipi.2021025

	A NOTE ON TRANSMISSION EIGENVALUES IN
	Cakoni, Fioralba 2; Meng, Shixu 1; Xiao, Jingni 2
刊名	INVERSE PROBLEMS AND IMAGING
	2021-10-01
卷号	15 期号:5 页码:999-1014
关键词	Key words and phrases Inverse problems Maxwell equations transmission eigenvalues scat-tering theory distribution of eigenvalues
ISSN号	1930-8337
DOI	10.3934/ipi.2021025
英文摘要	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.
资助项目	AFOSR[FA9550-20-1-0024] ; NSF[DMS-1813492]
WOS研究方向	Mathematics ; Physics
语种	英语
出版者	AMER INST MATHEMATICAL SCIENCES-AIMS
WOS记录号	WOS:000683552600008
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/59116]
专题	中国科学院数学与系统科学研究院
通讯作者	Xiao, Jingni
作者单位	1.Chinese Acad Sci, Inst Appl Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA
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.