期刊名称：IOP Conference Series: Earth and Environmental Science
印刷版ISSN：1755-1307
电子版ISSN：1755-1315
出版年度：2019
卷号：252
期号：3
页码：1-7
DOI：10.1088/1755-1315/252/3/032132
出版社：IOP Publishing
摘要：This paper investigates an inverse problem of using the additional conditions to reconstruct the first-order coefficient of the second order parabolic equation. Based on the optimal control framework, the existence of the minimize of the cost functional is proved, and the necessary condition which must be satisfied by the minimize is deduced. In the process of computation of the forward problem, a discrete finite difference scheme is constructed and the chasing method is applied to calculate the numerical solution. Finally, a numerical algorithm on the basis of the Gradient iterative method is designed to treat the inverse problem and some numerical experiments are also performed. The numerical results show that the algorithm designed in this paper is stable and that the coefficient is recovered very well.
