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INVERSE SOURCE PROBLEMS FOR THE STOCHASTIC WAVE EQUATIONS: FAR-FIELD PATTERNS
Li, Jianliang1; Li, Peijun2; Wang, Xu3,4
2022
发表期刊SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN0036-1399
卷号82期号:4页码:1113-1134
摘要This paper addresses the direct and inverse source problems for the stochastic acous-tic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally isotropic Gaussian random field, whose covariance and relation operators are classical pseudodifferential operators. Given the random source, the direct problems are shown to be well-posed in the sense of distributions and the regularity of the solutions are given. For the inverse problems, we demonstrate by ergodicity that the principal symbols of the covariance and relation operators can be uniquely determined by a single realization of the far-field pattern averaged over the frequency band with probability one.
关键词Key words inverse source problem stochastic wave equation Gaussian random field pseudodifferential operator far-field pattern uniqueness
DOI10.1137/21M1467663
收录类别SCI
语种英语
资助项目NNSF of China[12171057] ; NNSF of China[11871068] ; NNSF of China[DMS-1912704] ; NSF[11971470]
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000830588400001
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/61140
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.Yunnan Univ, Sch Math & Stat, Kunming 650091, Yunnan, Peoples R China
2.Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
3.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China
4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式
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Li, Jianliang,Li, Peijun,Wang, Xu. INVERSE SOURCE PROBLEMS FOR THE STOCHASTIC WAVE EQUATIONS: FAR-FIELD PATTERNS[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2022,82(4):1113-1134.
APA Li, Jianliang,Li, Peijun,&Wang, Xu.(2022).INVERSE SOURCE PROBLEMS FOR THE STOCHASTIC WAVE EQUATIONS: FAR-FIELD PATTERNS.SIAM JOURNAL ON APPLIED MATHEMATICS,82(4),1113-1134.
MLA Li, Jianliang,et al."INVERSE SOURCE PROBLEMS FOR THE STOCHASTIC WAVE EQUATIONS: FAR-FIELD PATTERNS".SIAM JOURNAL ON APPLIED MATHEMATICS 82.4(2022):1113-1134.
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