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Recovery of an embedded obstacle and the surrounding medium for Maxwell's system
Deng, Youjun1; Liu, Hongyu2; Liu, Xiaodong3
2019-08-05
Source PublicationJOURNAL OF DIFFERENTIAL EQUATIONS
ISSN0022-0396
Volume267Issue:4Pages:2192-2209
AbstractIn this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques. (C) 2019 Elsevier Inc. All rights reserved.
KeywordInverse electromagnetic scattering Maxwell system Embedded obstacle Surrounding medium Uniqueness
DOI10.1016/j.jde.2019.03.009
Language英语
Funding ProjectNSF grant of China[11601528] ; NSF grant of Hunan[2017JJ3432] ; Mathematics and Interdisciplinary Sciences Project, Central South University ; Hong Kong RGC General Research Funds[12302017] ; Hong Kong RGC General Research Funds[12302018] ; Youth Innovation Promotion Association CAS ; NNSF of China[11571355] ; Hong Kong Baptist University
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000468110200004
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34730
Collection应用数学研究所
Corresponding AuthorLiu, Hongyu
Affiliation1.Cent S Univ, Sch Math & Stat, Changsha, Hunan, Peoples R China
2.Hong Kong Baptist Univ, Dept Math, Kowloon, Hong Kong, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Deng, Youjun,Liu, Hongyu,Liu, Xiaodong. Recovery of an embedded obstacle and the surrounding medium for Maxwell's system[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2019,267(4):2192-2209.
APA Deng, Youjun,Liu, Hongyu,&Liu, Xiaodong.(2019).Recovery of an embedded obstacle and the surrounding medium for Maxwell's system.JOURNAL OF DIFFERENTIAL EQUATIONS,267(4),2192-2209.
MLA Deng, Youjun,et al."Recovery of an embedded obstacle and the surrounding medium for Maxwell's system".JOURNAL OF DIFFERENTIAL EQUATIONS 267.4(2019):2192-2209.
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