Numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation

被引：12
|
作者：
Jiang, Daijun [1 ,2 ]
Liu, Yikan [3 ]
Wang, Dongling [4 ,5 ]
机构：
[1] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China
[2] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China
[3] Hokkaido Univ, Res Inst Elect Sci, Res Ctr Math Social Creat, Kita Ward, N12W7, Sapporo, Hokkaido 0600812, Japan
[4] Northwest Univ, Dept Math, Xian 710075, Shaanxi, Peoples R China
[5] Northwest Univ, Ctr Nonlinear Studies, Xian 710075, Shaanxi, Peoples R China
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2020年 / 46卷 / 03期
基金：
日本学术振兴会; 中国国家自然科学基金;
关键词：
Time-fractional diffusion equation; Inverse source problem; Finite element method; Iterative thresholding algorithm; INVERSE SOURCE PROBLEM; WAVE EQUATIONS;
D O I：
10.1007/s10444-020-09754-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear minimization system by an appropriately selected Tikhonov regularization. The existence and the stability of the optimization system are demonstrated. The nonlinear optimization problem is approximated by a fully discrete scheme, whose convergence is established under a novel result verified in this study that the H-1-norm of the solution to the discrete forward system is uniformly bounded. The iterative thresholding algorithm is proposed to solve the discrete minimization, and several numerical experiments are presented to show the efficiency and the accuracy of the algorithm.
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页数：24
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