KMS Of Academy of mathematics and systems sciences, CAS
INVERSE ELASTIC SCATTERING FOR A RANDOM POTENTIAL\ast | |
LI, Jianliang1; LI, Peijun2; Wang, Xu3,4 | |
2022 | |
发表期刊 | SIAM JOURNAL ON MATHEMATICAL ANALYSIS |
ISSN | 0036-1410 |
卷号 | 54期号:5页码:5126-5159 |
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. |
关键词 | inverse scattering problem elastic wave equation generalized Gaussian random field pseudodifferential operator principal symbol uniqueness |
DOI | 10.1137/21M1430200 |
收录类别 | SCI |
语种 | 英语 |
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 |
WOS类目 | Mathematics, Applied |
WOS记录号 | WOS:000862265300002 |
出版者 | SIAM PUBLICATIONS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/60927 |
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.Hunan Normal Univ, Sch Math & Stat, Changsha 410081, Peoples R China 2.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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. |
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