Journal
APPLIED MATHEMATICAL MODELLING
Volume 39, Issue 23-24, Pages 7537-7553Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.03.016
Keywords
Inverse problem; Heat source; Uniqueness; Difference scheme; Landweber iteration; Numerical results
Funding
- National Natural Science Foundation (NNSF) of China [11061018, 11261029, 11461039]
- Youth Foundation of Lanzhou Jiaotong University [2011028]
- Long Yuan Young Creative Talents Support Program [252003]
- Natural Science Foundation (NSF) of Gansu Province of China [145RJZA124]
- Joint Funds of NSF of Gansu Province of China [1212RJZA043]
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This paper deals with an inverse problem of identifying the source coefficient in degenerate parabolic equations. On the basis of extremum principle, the uniqueness of the proposed problem is obtained. The difference scheme for the direct problem is got by using the finite volume method and the corresponding stability is also proved. An iteration scheme of the Landweber type is applied to handle the numerical solution. In the end, several numerical experiments are performed to test the validity of the scheme. The numerical results show that the method is stable and the unknown function is recovered very well when iterative parameter a and iterative times are matching appropriately. (C) 2015 Elsevier Inc. All rights reserved.
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