Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects

doi:10.1016/j.jde.2018.07.033

CSpace > 应用数学研究所

	Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects
	Yang, Jiaqing 1; Zhang, Bo2,3,4 ; Zhang, Haiwen3,5
	2018-12-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	265 期号:12 页码:6352-6383
摘要	This paper considers the inverse problem of scattering of time-harmonic acoustic and electromagnetic plane waves by a bounded, inhomogeneous, penetrable obstacle with embedded objects inside. A new method is proposed to prove that the inhomogeneous penetrable obstacle can be uniquely determined from the far-field pattern at a fixed frequency, disregarding its contents. Our method is based on constructing a well-posed interior transmission problem in a small domain associated with the Helmholtz or modified Helmholtz equation and the Maxwell or modified Maxwell equations. A key role is played by the smallness of the domain which ensures that the lowest transmission eigenvalue is large so that a given wave number k is not an eigenvalue of the interior transmission problem. Another ingredient in our proofs is a priori estimates of solutions to the transmission scattering problems with data in L-P (1 < p < 2), which are established in this paper by using the integral equation method. A main feature of the new method is that it can deal with the acoustic and electromagnetic cases in a unified way and can be easily applied to deal with inverse scattering by unbounded rough interfaces. (C) 2018 Elsevier Inc. All rights reserved.
DOI	10.1016/j.jde.2018.07.033
语种	英语
资助项目	NNSF of China[91630309] ; NNSF of China[11501558] ; NNSF of China[11771349] ; China Postdoctoral Science Foundation[2015M580827] ; China Postdoctoral Science Foundation[2016T90900] ; Postdoctoral research project of Shaanxi Province of China[2016BSHY-DZZ52]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000447902000010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/31349
专题	应用数学研究所
通讯作者	Zhang, Bo
作者单位	1.Xi An Jiao Tong Univ, Sch Math & Stat, Xian 710049, Shaanxi, Peoples R China 2.Chinese Acad Sci, LSEC, NCMIS, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 5.Chinese Acad Sci, NCMIS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Yang, Jiaqing,Zhang, Bo,Zhang, Haiwen. Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2018,265(12):6352-6383.
APA	Yang, Jiaqing,Zhang, Bo,&Zhang, Haiwen.(2018).Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects.JOURNAL OF DIFFERENTIAL EQUATIONS,265(12),6352-6383.
MLA	Yang, Jiaqing,et al."Uniqueness in inverse acoustic and electromagnetic scattering by penetrable obstacles with embedded objects".JOURNAL OF DIFFERENTIAL EQUATIONS 265.12(2018):6352-6383.