Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 236, Issue 17, Pages 4474-4484Publisher
ELSEVIER
DOI: 10.1016/j.cam.2012.04.019
Keywords
Inverse problem; Fractional diffusion equation; Ill-posed; Regularization
Categories
Funding
- National Natural Science Foundation of China [11001223, 11101335]
- Research Fund for the Doctoral Program of Higher Education of China [20106203120001]
- Chinese Ministry of Education [212179]
- Doctoral Foundation of Northwest Normal University, China [5002-577]
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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.
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