On isotropic cloaking and interior transmission eigenvalue problems

doi:10.1017/S0956792517000110

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 计算数学与科学工程计算研究所

	On isotropic cloaking and interior transmission eigenvalue problems
	Ji, Xia1 ; Liu, Hongyu 2,3
刊名	EUROPEAN JOURNAL OF APPLIED MATHEMATICS
	2018-04-01
卷号	29 期号:2 页码:253-280
关键词	Acoustic wave scattering invisibility cloaking isotropic and regular interior transmission eigenvalues
ISSN号	0956-7925
DOI	10.1017/S0956792517000110
英文摘要	This paper is concerned with the invisibility cloaking in acoustic wave scattering from a new perspective. We are especially interested in achieving the invisibility cloaking by completely regular and isotropic mediums. It is shown that an interior transmission eigenvalue problem arises in our study, which is the one considered theoretically in Cakoni et al. (Transmission eigenvalues for inhomogeneous media containing obstacles, Inverse Problems and Imaging, 6 (2012), 373-398). Based on such an observation, we propose a cloaking scheme that takes a three-layer structure including a cloaked region, a lossy layer and a cloaking shell. The target medium in the cloaked region can be arbitrary but regular, whereas the mediums in the lossy layer and the cloaking shell are both regular and isotropic. We establish that if a certain non-transparency condition is satisfied, then there exists an infinite set of incident waves such that the cloaking device is nearly invisible under the corresponding wave interrogation. The set of waves is generated from the Herglotz approximation of the associated interior transmission eigenfunctions. We provide both theoretical and numerical justifications.
资助项目	FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Fund[12302415] ; NSFC[11371115] ; National Natural Science Foundation of China[11271018] ; National Natural Science Foundation of China[91230203] ; Special Funds for National Basic Research Program of China, 973 Program[2012CB025904]
WOS研究方向	Mathematics
语种	英语
出版者	CAMBRIDGE UNIV PRESS
WOS记录号	WOS:000426855300003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/29749]
专题	计算数学与科学工程计算研究所
通讯作者	Ji, Xia
作者单位	1.Chinese Acad Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China 2.Hong Kong Baptist Univ, Dept Math, Kowloon Tong, Hong Kong, Peoples R China 3.Virtual Univ Pk, HKBU Inst Res & Continuing Educ, Shenzhen, Peoples R China
推荐引用方式 GB/T 7714	Ji, Xia,Liu, Hongyu. On isotropic cloaking and interior transmission eigenvalue problems[J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS,2018,29(2):253-280.
APA	Ji, Xia,&Liu, Hongyu.(2018).On isotropic cloaking and interior transmission eigenvalue problems.EUROPEAN JOURNAL OF APPLIED MATHEMATICS,29(2),253-280.
MLA	Ji, Xia,et al."On isotropic cloaking and interior transmission eigenvalue problems".EUROPEAN JOURNAL OF APPLIED MATHEMATICS 29.2(2018):253-280.