On a Backward Problem for the Rayleigh-Stokes Equation with a Fractional Derivative

被引：0

作者：

Liu, Songshu ^{[1
]}

Liu, Tao ^{[1
]}

Ma, Qiang ^{[2
]}

机构：

[1] Northeastern Univ Qinhuangdao, Sch Math & Stat, Qinhuangdao 066004, Peoples R China

[2] Harbin Inst Technol Weihai, Dept Math, Weihai 264209, Peoples R China

来源：

AXIOMS | 2024年 / 13卷 / 01期

关键词：

Rayleigh-Stokes equation with a fractional derivative; backward problem; Tikhonov regularization method; convergence estimate; GENERALIZED 2ND-GRADE FLUID; TIKHONOV REGULARIZATION METHOD; 1ST PROBLEM; ORDER;

D O I：

10.3390/axioms13010030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Rayleigh-Stokes equation with a fractional derivative is widely used in many fields. In this paper, we consider the inverse initial value problem of the Rayleigh-Stokes equation. Since the problem is ill-posed, we adopt the Tikhonov regularization method to solve this problem. In addition, this paper not only analyzes the ill-posedness of the problem but also gives the conditional stability estimate. Finally, the convergence estimates are proved under two regularization parameter selection rules.

引用

页数：12

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