Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 235, Issue 15, Pages 4404-4417Publisher
ELSEVIER
DOI: 10.1016/j.cam.2011.04.006
Keywords
Inverse problem; Degenerate parabolic equation; Uniqueness; Predictor-corrector method; Numerical results
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Funding
- NNSF of China [11061018, 10972095]
- NSF of Gansu Province of China [0916RJZA046]
- Fundamental Research Funds for Universities in the Gansu Province of China [620004]
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This work studies an inverse problem of determining the first-order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point. Being different from other ordinary parameter identification problems in parabolic equations, in our mathematical model there exists degeneracy on the lateral boundaries of the domain, which may cause the corresponding boundary conditions to go missing. By the contraction mapping principle, the uniqueness of the solution for the inverse problem is proved. A numerical algorithm on the basis of the predictor-corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown function is recovered very well. The results obtained in the paper are interesting and useful, and can be extended to other more general inverse coefficient problems of degenerate PDEs. (C) 2011 Elsevier B.V. All rights reserved.
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