数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (4): 1012-1024.doi: 10.1016/S0252-9602(14)60065-5

• 论文 • 上一篇    下一篇

IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

杨帆1,2*|傅初黎2|李晓晓1   

  1. 1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China;
    2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2013-07-30 出版日期:2014-07-20 发布日期:2014-07-20
  • 通讯作者: 杨帆,yfggd114@163.com E-mail:yfggd114@163.com; fuchuli@lzu.edu.cn; lixiaoxiaogood@126.com
  • 基金资助:

    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.

IDENTIFYING AN UNKNOWN SOURCE IN SPACE-FRACTIONAL DIFFUSION EQUATION

 YANG Fan1,2*, FU Chu-Li2, LI Xiao-Xiao1   

  1. 1. School of Science, Lanzhou University of Technology, Lanzhou 730050, China;
    2. School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
  • Received:2013-07-30 Online:2014-07-20 Published:2014-07-20
  • Contact: YANG Fan,yfggd114@163.com E-mail:yfggd114@163.com; fuchuli@lzu.edu.cn; lixiaoxiaogood@126.com
  • 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.

摘要:

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.

关键词: spatial-dependent heat source, space-fractional diffusion equation, generalized Tikhonov regularization, A posteriori parameter choice, error estimate

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.

Key words: spatial-dependent heat source, space-fractional diffusion equation, generalized Tikhonov regularization, A posteriori parameter choice, error estimate

中图分类号: 

  • 35R30