识别Rayleigh-Stokes方程源项的分数阶Landweber迭代正则化方法

摘要/Abstract

摘要：

该文研究具有Riemann-Liouville时间分数阶导数的Rayleigh-Stokes方程未知源识别问题.首先证明这个问题是不适定的，并应用分数阶Landweber正则化方法求解此反问题.基于条件稳定性结果，在先验和后验正则化参数选取规则下，分别给出精确解与正则解之间的误差估计.最后通过数值例子说明此方法求解此类反问题的有效性和可行性.

关键词: Rayleigh-Stokes方程, 反问题, 识别源项, 分数阶Landweber迭代正则化方法

Abstract:

In this paper, the inverse problem of identifying the unknown sources for the Rayleigh-Stokes equation with a Riemann-Liouville fractional derivative in time is considered. We prove that such a problem is ill-posed and apply the fractional Landweber method to solve this inverse problem. Based on the results of conditional stability, under the priori and posteriori regularization parameters choice rules, the error estimates between the exact solution and the regularization solution are given respectively. Finally, several numerical examples are given to illustrate the effectiveness and feasibility of these methods.

Key words: Rayleigh-Stokes equation, Inverse problem, Identifying unknown source problem, Fractional Landweber iterative regularization method

中图分类号:

O175

杨帆,王乾朝,李晓晓. 识别Rayleigh-Stokes方程源项的分数阶Landweber迭代正则化方法[J]. 数学物理学报, 2021, 41(2): 427-450.

Fan Yang,Qianchao Wang,Xiaoxiao Li. Fractional Landweber Iterative Regularization Method to Identify Source Term for the Rayleigh-Stokes Equation[J]. Acta mathematica scientia,Series A, 2021, 41(2): 427-450.

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