期刊
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
卷 33, 期 6, 页码 1900-1923出版社
WILEY
DOI: 10.1002/num.22165
关键词
Degenerate parabolic equation; inverse problem; initial value; Landweber iteration; numerical results
资金
- National Natural Science Foundation of China [11261029, 11461039, 61663018]
- Long Yuan Young Creative Talents Support Program [252003]
- NSF of Gansu Province of China [145RJZA124]
This work studies the inverse problem of reconstructing an initial value function in the degenerate parabolic equation using the final measurement data. Problems of this type have important applications in the field of financial engineering. Being different from other inverse backward parabolic problems, the mathematical model in our article may be allowed to degenerate at some part of boundaries, which may lead to the corresponding boundary conditions missing. The conditional stability of the solution is obtained using the logarithmic convexity method. A finite difference scheme is constructed to solve the direct problem and the corresponding stability and convergence are proved. The Landweber iteration algorithm is applied to the inverse problem and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown initial value is recovered very well.(c) 2017 Wiley Periodicals, Inc.
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