Inverse source problem for a fractional diffusion equation

被引：220
|
作者：
Zhang, Ying [1 ]
Xu, Xiang [1 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
来源：
INVERSE PROBLEMS | 2011年 / 27卷 / 03期
关键词：
RANDOM-WALKS; TRANSPORT; DISPERSION; PRINCIPLE;
D O I：
10.1088/0266-5611/27/3/035010
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An inverse source problem for a fractional diffusion equation is investigated. Under an assumption that the unknown source term is time independent, an analytical solution can be deduced based on the method of the eigenfunction expansion. Then, the uniqueness of the inverse problem is proved by analytic continuation and Laplace transform. Regularization schemes are considered to obtain the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed meshless method.
引用
收藏
页数：12
相关论文
共 50 条
  • [1] An Inverse Source Problem of Space-Fractional Diffusion Equation
    Liu, Songshu
    Feng, Lixin
    Zhang, Guilai
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (06) : 4405 - 4424
  • [2] AN INVERSE SOURCE PROBLEM FOR A GENERALIZED TIME FRACTIONAL DIFFUSION EQUATION
    Faizi, R.
    Atmania, R.
    [J]. EURASIAN JOURNAL OF MATHEMATICAL AND COMPUTER APPLICATIONS, 2022, 10 (01): : 26 - 39
  • [3] INVERSE SOURCE PROBLEM WITH A FINAL OVERDETERMINATION FOR A FRACTIONAL DIFFUSION EQUATION
    Sakamoto, Kenichi
    Yamamoto, Masahiro
    [J]. MATHEMATICAL CONTROL AND RELATED FIELDS, 2011, 1 (04) : 509 - 518
  • [4] An inverse random source problem in a stochastic fractional diffusion equation
    Niu, Pingping
    Helin, Tapio
    Zhang, Zhidong
    [J]. INVERSE PROBLEMS, 2020, 36 (04)
  • [5] An Inverse Source Problem of Space-Fractional Diffusion Equation
    Songshu Liu
    Lixin Feng
    Guilai Zhang
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 4405 - 4424
  • [6] Inverse problem for fractional diffusion equation
    Vu Kim Tuan
    [J]. Fractional Calculus and Applied Analysis, 2011, 14 : 31 - 55
  • [7] INVERSE PROBLEM FOR FRACTIONAL DIFFUSION EQUATION
    Vu Kim Tuan
    [J]. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2011, 14 (01) : 31 - 55
  • [8] An inverse problem for a fractional diffusion equation
    Xiong, Xiangtuan
    Guo, Hongbo
    Liu, Xiaohong
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (17) : 4474 - 4484
  • [9] Inverse source problem for a diffusion equation involving the fractional spectral Laplacian
    BenSalah, Mohamed
    Hassine, Maatoug
    [J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (01) : 917 - 936
  • [10] INverse Source Problem for a Space-Time Fractional Diffusion Equation
    Muhammad Ali
    Sara Aziz
    Salman A. Malik
    [J]. Fractional Calculus and Applied Analysis, 2018, 21 : 844 - 863
12345