Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 393, Issue 1, Pages 185-199Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2012.03.013
Keywords
Time-fractional diffusion equation; Ill-posedness; Stability estimate; Regularization; Numerical approximation
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Funding
- Research Council of the Hong Kong Special Administrative Region, China [CityU 101310]
- National Natural Science Foundation of China [11001223, 11101335]
- Research Fund for the Doctoral Program of Higher Education of China [20106203120001]
- Chinese Ministry of Education [2012-179]
- Doctoral Foundation of Northwest Normal University, China [5002-577]
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In this paper we investigate an inverse problem for a time-fractional diffusion equation which is highly ill-posed in the two-dimensional setting. Based on an a priori assumption, we give a conditional stability result. Some new regularization methods are constructed for solving the inverse problem and the corresponding error estimates are proved. For numerical illustration, several examples are constructed to demonstrate the feasibility and efficiency of the proposed methods. (C) 2012 Elsevier Inc. All rights reserved.
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