期刊
APPLIED NUMERICAL MATHEMATICS
卷 87, 期 -, 页码 1-19出版社
ELSEVIER
DOI: 10.1016/j.apnum.2014.08.001
关键词
Inverse problem; Fractional derivative; Uniqueness; Regularization; Convergence; Numerics
资金
- NSFC [91330109, 11201066]
- NSF of Jiangsu Province [BK2011584, BK2012320]
- Grants-in-Aid for Scientific Research [15H05740, 15K13455] Funding Source: KAKEN
Consider an inverse problem for the time-fractional diffusion equation in one dimensional spatial space. The aim is to determine the initial status and heat flux on the boundary simultaneously from heat measurement data given on the other boundary. Using the Laplace transform and the unique extension technique, the uniqueness for this inverse problem is proven. Then we construct a regularizing scheme for the reconstruction of boundary flux for known initial status. The convergence rate of the regularizing solution is established under some a priori information about the exact solution. Moreover, the initial distribution can also be recovered approximately from our regularizing scheme. Finally we present some numerical examples, which show the validity of the proposed reconstruction scheme. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.
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