Identifying an unknown source in time-fractional diffusion equation by a truncation method

被引：78
作者：
Zhang, Z. Q. [1 ]
Wei, T. [1 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2013年 / 219卷 / 11期
关键词：
Ill-posed problem; Fractional diffusion equation; Inverse source problem; Truncation method; Discrepancy principle; REGULARIZATION METHOD; ANOMALOUS DIFFUSION; CAUCHY-PROBLEM; RANDOM-WALKS; SOURCE-TERM; PRINCIPLE;
D O I：
10.1016/j.amc.2012.12.024
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, an inverse source problem for the time-fractional diffusion equation is investigated. We prove a conditional stability for this problem. A truncation method is presented to deal with the ill-posedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable. (C) 2012 Elsevier Inc. All rights reserved.
引用
收藏
页码：5972 / 5983
页数：12
相关论文
共 43 条
  • [1] [Anonymous], 1989, DIFFER EQU
  • [2] [Anonymous], 1999, FRACTIONAL DIFFERENT
  • [3] [Anonymous], 1995, J INV ILL POSED PROB
  • [4] From continuous time random walks to the fractional Fokker-Planck equation
    Barkai, E
    Metzler, R
    Klafter, J
    [J]. PHYSICAL REVIEW E, 2000, 61 (01) : 132 - 138
  • [5] Anomalous transport in laboratory-scale, heterogeneous porous media
    Berkowitz, B
    Scher, H
    Silliman, SE
    [J]. WATER RESOURCES RESEARCH, 2000, 36 (01) : 149 - 158
  • [6] Determination of the unknown sources in the heat-conduction equation
    Burykin A.A.
    Denisov A.M.
    [J]. Computational Mathematics and Modeling, 1997, 8 (4) : 309 - 313
  • [7] AN INVERSE PROBLEM FOR THE HEAT-EQUATION
    CANNON, JR
    ESTEVA, SP
    [J]. INVERSE PROBLEMS, 1986, 2 (04) : 395 - 403
  • [8] Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation
    Cheng, Jin
    Nakagawa, Junichi
    Yamamoto, Masahiro
    Yamazaki, Tomohiro
    [J]. INVERSE PROBLEMS, 2009, 25 (11)
  • [9] Numerical inversions of a source term in the FADE with a Dirichlet boundary condition using final observations
    Chi, Guangsheng
    Li, Gongsheng
    Jia, Xianzheng
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (04) : 1619 - 1626
  • [10] Wavelet and Fourier methods for solving the sideways heat equation
    Eldén, L
    Berntsson, F
    Reginska, T
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 21 (06) : 2187 - 2205
12345