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INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast

文献类型：期刊论文

作者LI, Jianliang2; LI, Peijun3; Wang, Xu1,4
刊名SIAM JOURNAL ON MATHEMATICAL ANALYSIS
出版日期2022
卷号54期号:5页码:5126-5159
ISSN号0036-1410
关键词inverse scattering problem elastic wave equation generalized Gaussian random field pseudodifferential operator principal symbol uniqueness
DOI10.1137/21M1430200
英文摘要This paper is concerned with an inverse scattering problem for the time-harmonic elastic wave equation with a random potential. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic generalized Gaussian random field with the covariance operator being described by a classical pseudodifferential operator. The goal is to determine the principal symbol of the covariance operator from the scattered wave measured in a bounded domain which has a positive distance from the domain of the potential. For such a rough potential, the well-posedness of the direct scattering problem in the distribution sense is established by studying an equivalent LippmannSchwinger integral equation. For the inverse scattering problem, it is shown with probability one that the principal symbol of the covariance operator can be uniquely determined by the amplitude of the scattered waves averaged over the frequency band from a single realization of the random potential. The analysis employs the Born approximation in high frequency, asymptotics of the Green tensor for the elastic wave equation, and microlocal analysis for the Fourier integral operators.
资助项目National Natural Science Foundation of China (NFSC)[12171057] ; National Science Foundation (NSF)[DMS-1912704] ; National Science Foundation (NSF)[DMS-2208256] ; NFSC[11971470] ; NFSC[11871068]
WOS研究方向Mathematics
语种英语
出版者SIAM PUBLICATIONS
WOS记录号WOS:000862265300002
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/60926]  
专题中国科学院数学与系统科学研究院
通讯作者LI, Jianliang
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China
3.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
4.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 LI, Jianliang,LI, Peijun,Wang, Xu. INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS,2022,54(5):5126-5159.
APA LI, Jianliang,LI, Peijun,&Wang, Xu.(2022).INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast.SIAM JOURNAL ON MATHEMATICAL ANALYSIS,54(5),5126-5159.
MLA LI, Jianliang,et al."INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast".SIAM JOURNAL ON MATHEMATICAL ANALYSIS 54.5(2022):5126-5159.

入库方式： OAI收割

来源：数学与系统科学研究院

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