Stability for Inverse Source Problems of the Stochastic Helmholtz Equation with a White Noise

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-04-11 DOI:10.1137/23m1586331

Peijun Li, Ying Liang

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 687-709, April 2024.
Abstract. This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.

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带有白噪声的随机亥姆霍兹方程反源问题的稳定性

SIAM 应用数学杂志》第 84 卷第 2 期第 687-709 页，2024 年 4 月。摘要本文主要研究白噪声驱动的随机亥姆霍兹方程反源问题的稳定性估计。针对直接源问题建立了良好拟合，从而确保了解的存在性和唯一性。推导出了逆源问题的稳定性估计，其目的是确定随机源的强度。为了增强反源问题的稳定性，我们纳入了有关强度的规则性和支持性的先验信息。在均质介质的情况下，我们建立了霍尔德稳定性估计，为重建源强度提供了稳定性的量化指标。对于非均质介质这种更具挑战性的情况，则提出了对数稳定性估计，以捕捉源和不同介质特性之间错综复杂的相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.