Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 218, Issue 2, Pages 396-405Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.05.076
Keywords
Spectral regularization; Time-fractional inverse diffusion; Caputo's fractional derivatives; Temperature; Heat flux; Fourier transform; Laplace transform
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Funding
- GS1NSF of China [10971089]
- Fundamental Research Funds for the Central Universities [lzujbky-2010-k10]
- Lanzhou University
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In this paper, we consider an inverse problem for a time-fractional diffusion equation with one-dimensional semi-infinite domain. The temperature and heat flux are sought from a measured temperature history at a fixed location inside the body. We show that such problem is severely ill-posed and further apply a spectral regularization method to solve it based on the solution given by the Fourier method. Convergence estimates are presented under a priori bound assumptions for the exact solution. Finally, numerical examples are given to show that the proposed numerical method is effective. (C) 2011 Elsevier Inc. All rights reserved.
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