On isotropic cloaking and interior transmission eigenvalue problems

doi:10.1017/S0956792517000110

	On isotropic cloaking and interior transmission eigenvalue problems
	Ji, Xia1 ; Liu, Hongyu 2,3
	2018-04-01
发表期刊	EUROPEAN JOURNAL OF APPLIED MATHEMATICS
ISSN	0956-7925
卷号	29 期号:2 页码:253-280
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.
关键词	Acoustic wave scattering invisibility cloaking isotropic and regular interior transmission eigenvalues
DOI	10.1017/S0956792517000110
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000426855300003
出版者	CAMBRIDGE UNIV PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29750
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.