AN INVERSE SOURCE PROBLEM FOR THE STOCHASTIC WAVE EQUATION

被引：4

作者：

Feng, Xiaoli ^{[1
]}

Zhao, Meixia ^{[1
]}

Li, Peijun ^{[2
]}

Wang, Xu ^{[2
]}

机构：

[1] Xidian Univ, Sch Math & Stat, Xian 713200, Peoples R China

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2022年 / 16卷 / 02期

关键词：

  Stochastic wave equation; inverse source problem; fractional Brownian motion; uniqueness; ill-posedness; HYPERBOLIC PROBLEM; GLOBAL UNIQUENESS; STABILITY; DRIVEN; FORMULATION;

D O I：

10.3934/ipi.2021055

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with an inverse source problem for the stochastic wave equation driven by a fractional Brownian motion. Given the random source, the direct problem is to study the solution of the stochastic wave equation. The inverse problem is to determine the statistical properties of the source from the expectation and covariance of the final-time data. For the direct problem, it is shown to be well-posed with a unique mild solution. For the inverse problem, the uniqueness is proved for a certain class of functions and the instability is characterized. Numerical experiments are presented to illustrate the reconstructions by using a truncation-based regularization method.

引用

页码：397 / 415

页数：19

共 43 条

[1] An inverse source problem for Maxwell's equations in magnetoencephalography [J].

Ammari, H ;

Bao, G ;

Fleming, JL .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2002, 62 (04) :1369-1382

[2] Application of inverse source concepts to photoacoustic tomography [J].

Anastasio, Mark A. ;

Zhang, Jin ;

Modgil, Dimple ;

La Riviere, Patrick J. .

INVERSE PROBLEMS, 2007, 23 (06) :S21-S35

[3]

Baker Alan., 1990, Transcendental number theory

[4] INVERSE RANDOM SOURCE SCATTERING FOR ELASTIC WAVES [J].

Bao, Gang ;

Chen, Chuchu ;

Li, Peijun .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2017, 55 (06) :2616-2643

[5] Inverse Random Source Scattering Problems in Several Dimensions [J].

Bao, Gang ;

Chen, Chuchu ;

Li, Peijun .

SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2016, 4 (01) :1263-1287

[6]

Bao G, 2014, MATH COMPUT, V83, P215

[7] An inverse source problem with multiple frequency data [J].

Bao, Gang ;

Lin, Junshan ;

Triki, Faouzi .

COMPTES RENDUS MATHEMATIQUE, 2011, 349 (15-16) :855-859

[8] A multi-frequency inverse source problem [J].

Bao, Gang ;

Lin, Junshan ;

Triki, Faouzi .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 249 (12) :3443-3465

[9]

BUKHGEIM AL, 1981, DOKL AKAD NAUK SSSR+, V260, P269

[10] The stochastic wave equation driven by fractional Brownian noise and temporally correlated smooth noise [J].

Caithamer, P .

STOCHASTICS AND DYNAMICS, 2005, 5 (01) :45-64

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