1. Identifying the diffusion coefficient by optimization from the final observation
- Author
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Deng, Zui-Cha, Yang, Liu, Yu, Jian-Ning, and Luo, Guan-Wei
- Subjects
- *
DIFFUSION , *COEFFICIENTS (Statistics) , *MATHEMATICAL optimization , *INVERSE problems , *REACTION-diffusion equations , *BOUNDARY value problems - Abstract
Abstract: This paper deals with the inverse problem of determining a pair in the reaction–diffusion equationwith initial and boundary conditionsfrom the final measurement data , which has important application in a large fields of applied science. Based on the optimal control framework, the existence, uniqueness and stability of the minimizer for the cost functional are established. A necessary condition which is a couple system of a parabolic equation and a parabolic variational inequality is deduced. The gradient iteration algorithm is applied to the inverse problem and some numerical results are presented for various typical test examples. [Copyright &y& Elsevier]
- Published
- 2013
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