A backward problem for stochastic Kuramoto-Sivashinsky equation: Conditional stability and numerical solution

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-10-22 DOI:10.1016/j.jmaa.2024.128988

Zewen Wang , Weili Zhu , Bin Wu , Bin Hu

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引用次数: 0

Abstract

In this paper, we consider a backward problem in time for a linear stochastic Kuramoto-Sivashinsky equation. Firstly, we present two Carleman estimates incorporating weight functions independent of the variable x for the stochastic Kuramoto-Sivashinsky equation. Subsequently, we employ these two Carleman estimates to establish conditional stability for the backward problem in two distinct scenarios: when

0 < t_{0} < T

and when

t_{0} = 0

. Lastly, we transform the backward problem in time into the minimization of a regularized Tikhonov functional. This functional is solved by the conjugate gradient algorithm based on the gradient formula tailored for the regularized functional. Numerical examples related to the recovery of continuous and discontinuous initial values illustrate the effectiveness of the conjugate gradient algorithm.

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随机 Kuramoto-Sivashinsky 方程的后向问题：条件稳定性和数值解

在本文中，我们考虑了线性随机 Kuramoto-Sivashinsky 方程的时间反演问题。首先，我们为随机 Kuramoto-Sivashinsky 方程提出了两个 Carleman 估计值，其中包含与变量 x 无关的权重函数。随后，我们利用这两个卡勒曼估计值建立了后向问题在两种不同情况下的条件稳定性：0<t0<T 时和 t0=0 时。该函数通过共轭梯度算法求解，该算法基于为正则化函数量身定制的梯度公式。与恢复连续和不连续初始值有关的数值示例说明了共轭梯度算法的有效性。

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

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.