An Inverse Random Source Problem for the Biharmonic Wave Equation

被引:8
作者
Li, Peijun [1 ]
Wang, Xu [2 ,3 ]
机构
[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[2] Chinese Acad Sci, Acad Math & Syst Sci, LSEC, ICMSEC, Beijing 100190, Peoples R China
[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
基金
中国国家自然科学基金;
关键词
inverse random source problem; biharmonic operator; Gaussian random fields; stochastic differential equations; pseudo-differential operator; principal symbol; 1ST-ORDER PERTURBATION; SCATTERING; OPERATOR;
D O I
10.1137/21M1429138
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper is concerned with an inverse source problem for the stochastic biharmonic wave equation. The driven source is assumed to be a microlocally isotropic Gaussian random field with its covariance operator being a classical pseudo-differential operator. The well-posedness of the direct problem is examined in the distribution sense, and the regularity of the solution is discussed for the given rough source. For the inverse problem, the strength of the random source, involved in the principal symbol of its covariance operator, is shown to be uniquely determined by a single realization of the magnitude of the wave field averaged over the frequency band with probability one. Numerical experiments are presented to illustrate the validity and effectiveness of the proposed method for the case that the random source is white noise.
引用
收藏
页码:949 / 974
页数:26
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