Articles

IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

  • YANG Fan ,
  • FU Chu-Li ,
  • LI Xiao-Xiao
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  • 1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China;
    2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China

Received date: 2013-07-30

  Online published: 2014-07-20

Supported by

The project is supported by the National Natural Science Foundation of China (11171136, 11261032), the Distinguished Young Scholars Fund of Lan Zhou University of Technology (Q201015) and the basic scientific research business expenses of Gansu province college.

Abstract

In this paper, we identify a space-dependent source for a fractional diffusion equation. This problem is ill-posed, i.e., the solution (if it exists) does not depend continu-ously on the data. The generalized Tikhonov regularization method is proposed to solve this problem. An a priori error estimate between the exact solution and its regularized approxi-mation is obtained. Moreover, an a posteriori parameter choice rule is proposed and a stable error estimate is also obtained. Numerical examples are presented to illustrate the validity and effectiveness of this method.

Cite this article

YANG Fan , FU Chu-Li , LI Xiao-Xiao . IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION[J]. Acta mathematica scientia, Series B, 2014 , 34(4) : 1012 -1024 . DOI: 10.1016/S0252-9602(14)60065-5

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