Stability on the inverse random source scattering problem for the one-dimensional Helmholtz equation

被引：23

作者：

Li, Peijun ^{[1
]}

Yuan, Ganghua ^{[2
]}

机构：

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

[2] Northeast Normal Univ, Sch Math & Stat, KLAS, Changchun 130024, Jilin, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 450卷 / 02期

基金：

美国国家科学基金会;

关键词：

Stability; Inverse source problem; Helmholtz equation; Stochastic differential equation; NONUNIQUENESS;

D O I：

10.1016/j.jmaa.2017.01.074

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the one-dimensional stochastic Helmholtz equation where the source is assumed to be driven by the white noise. This paper concerns the stability analysis of the inverse random source problem which is to reconstruct the statistical properties of the source such as the mean and variance. Our results show that increasing stability can be obtained for the inverse problem by using suitable boundary data with multi-frequencies. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：872 / 887

页数：16

共 14 条

[1]

[Anonymous], 2006, Stochastic Differential Equations and Applications

[2] Inverse scattering problems with multi-frequencies [J].