An efficient iterative quasi-reversibility method for the inverse source problem of time-fractional diffusion equations

被引：1

作者：

Wen, Jin ^{[1
,3
]}

Liu, Yun-Long ^{[1
]}

O'Regan, Donal ^{[2
]}

机构：

[1] Northwest Normal Univ, Dept Math, Lanzhou, Peoples R China

[2] Univ Galway, Sch Math & Stat Sci, Galway, Ireland

[3] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

来源：

NUMERICAL HEAT TRANSFER PART B-FUNDAMENTALS | 2025年 / 86卷 / 04期

关键词：

Error estimate; inverse source problem; iterative quasi-reversibility; Morozov's discrepancy principle; SPACE-DEPENDENT SOURCE; REGULARIZATION METHOD; ANOMALOUS TRANSPORT; SOURCE-TERM; UNIQUENESS;

D O I：

10.1080/10407790.2024.2306264

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

This paper is devoted to recovering the source term for a time-fractional diffusion equation from additional temperature data at fixed time t=1. We discuss a uniqueness result of the direct problem and the ill-posedness of the inverse problem, and then apply the iterative quasi-reversibility regularization method to solve the inverse problem. Finally, some one-dimensional and two-dimensional numerical examples are given to verify the effectiveness and feasibility of the proposed method.

引用

页码：1158 / 1175

页数：18

共 40 条

[21] An inverse source problem in a semilinear time-fractional diffusion equation [J].

Slodicka, M. ;

Siskova, K. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (06) :1655-1669

[22] From diffusion to anomalous diffusion: A century after Einstein's Brownian motion [J].

Sokolov, IM ;

Klafter, J .

CHAOS, 2005, 15 (02)

[23] An inverse source problem for a one-dimensional space-time fractional diffusion equation [J].

Tatar, Salih ;

Ulusoy, Suleyman .

APPLICABLE ANALYSIS, 2015, 94 (11) :2233-2244

[24] The quasi-reversibility method for an inverse source problem for time-space fractional parabolic equations [J].

Van Duc, Nguyen ;

Van Thang, Nguyen ;

Thanh, Nguyen Trung .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2023, 344 :102-130

[25] Quasi-reversibility method to identify a space-dependent source for the time-fractional diffusion equation [J].

Wang, Jun-Gang ;

Wei, Ting .

APPLIED MATHEMATICAL MODELLING, 2015, 39 (20) :6139-6149

[26] An Iterative Method for Backward Time-Fractional Diffusion Problem [J].

Wang, Jun-Gang ;

Wei, Ting .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2014, 30 (06) :2029-2041

[27] EXPONENTIAL TIKHONOV REGULARIZATION METHOD FOR SOLVING AN INVERSE SOURCE PROBLEM OF TIME FRACTIONAL DIFFUSION EQUATION [J].

Wang, Zewen ;

Qiu, Shufang ;

Yu, Shuang ;

Wu, Bin ;

Zhang, Wen .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2023, 41 (02) :173-190

[28] An inverse time-dependent source problem for a time-fractional diffusion equation [J].

Wei, T. ;

Li, X. L. ;

Li, Y. S. .

INVERSE PROBLEMS, 2016, 32 (08)

[29] The backward problem for a time-fractional diffusion-wave equation in a bounded domain [J].

Wei, Ting ;

Zhang, Yun .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (10) :3632-3648

[30] Uniqueness for an inverse space-dependent source term in a multi-dimensional time-fractional diffusion equation [J].

Wei, Ting ;

Sun, Liangliang ;

Li, Yushan .

APPLIED MATHEMATICS LETTERS, 2016, 61 :108-113

← 1 2 3 4 →