An inverse problem for a fractional diffusion equation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Xiong, Xiangtuan¹  Guo, Hongbo¹  Liu, Xiaohong¹ 

[1] NW Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China

关键词: Inverse problem;    Fractional diffusion equation;    Ill-posed;    Regularization;   

DOI  :  10.1016/j.cam.2012.04.019

来源: Elsevier

【 摘 要 】

In this paper, we consider an inverse problem for a fractional diffusion equation which is highly ill-posed. Such a problem is obtained from the classical diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative of order alpha (0 < alpha < 1). We show that the problem is severely ill-posed and further apply an optimal regularization method to solve it based on the solution in the frequency domain. We can prove the optimal convergence estimate, which shows that the regularized solution depends continuously on the data and is a good approximation to the exact solution. Numerical examples show that the proposed method works well. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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