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

共 32 条

[1] Identification of source term for the Rayleigh-Stokes problem with Gaussian random noise [J].

Anh Triet Nguyen ;

Vu Cam Hoan Luu ;

Hoang Luc Nguyen ;

Huy Tuan Nguyen ;

Van Thinh Nguyen .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (14) :5593-5601

[2]

[Anonymous], 1999, Fractional differential equations

[3] An analysis of the Rayleigh-Stokes problem for a generalized second-grade fluid [J].

Bazhlekova, Emilia ;

Jin, Bangti ;

Lazarov, Raytcho ;

Zhou, Zhi .

NUMERISCHE MATHEMATIK, 2015, 131 (01) :1-31

[4] Numerical methods of the variable-order Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivative [J].

Chen, Chang-Ming ;

Liu, F. ;

Burrage, K. ;

Chen, Y. .

IMA JOURNAL OF APPLIED MATHEMATICS, 2013, 78 (05) :924-944

[5] Numerical methods with fourth-order spatial accuracy for variable-order nonlinear Stokes' first problem for a heated generalized second grade fluid [J].

Chen, Chang-Ming ;

Liu, F. ;

Turner, I. ;

Anh, V. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) :971-986

[6] A finite element method for the numerical solution of Rayleigh-Stokes problem for a heated generalized second grade fluid with fractional derivatives [J].

Dehghan, Mehdi ;

Abbaszadeh, Mostafa .

ENGINEERING WITH COMPUTERS, 2017, 33 (03) :587-605

[7] An improved finite difference/finite element method for the fractional Rayleigh-Stokes problem with a nonlinear source term [J].

Guan, Zhen ;

Wang, Xiaodong ;

Ouyang, Jie .

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2021, 65 (1-2) :451-479

[8]

Hilfer R., 2000, Applications of Fractional Calculus in Physics, DOI DOI 10.1142/3779

[9] Regularity of the solution for a final value problem for the Rayleigh-Stokes equation [J].

Hoang Luc Nguyen ;

Huy Tuan Nguyen ;

Zhou, Yong .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (10) :3481-3495

[10] Identifying initial condition of the Rayleigh-Stokes problem with random noise [J].

Hoang Luc Nguyen ;

Huy Tuan Nguyen ;

Mokhtar, Kirane ;

Xuan Thanh Duong Dang .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2019, 42 (05) :1561-1571

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