%0 Journal Article
%T 一类Kolmogorov型方程的系数反演问题<br>An inverse problem of identifying the coefficient in a Kolmogorov type equation
%A 蔡超
%J 山东大学学报（理学版）
%D 2016
%R 10.6040/j.issn.1671-9352.0.2015.268
%X 摘要： 研究了一类Kolmogorov型方程的对流系数反演问题,这类问题在很多科学研究和工程领域都有重要的应用,其特点是未知系数是同时依赖于空间变量x和时间变量t的函数。基于最优控制理论框架下,先将原问题转化为一个优化问题,并证明了控制泛函最优解的存在性及它满足的必要条件,然后证明了最优解的稳定性和唯一性。<br>Abstract: This work investigates an inverse problem of reconstructing the convection coefficient in a Kolmogorov equation from the final measurement data, which has important application in many fields of applied science. Compared with ordinary inverse problems, the unknown coefficient in this work depends on both the space variable x and the time variable t. On the basis of the optimal control framework, the identification problem is transformed into an optimization problem and the existence of the minimizer for the cost functional is established. Then necessary condition of the minimizer is obtained. After the necessary condition of the minimizer satisfied, the stability and uniqueness of the minimizer are deduced
%K Kolmogorov型方程
%K 存在性
%K 唯一性
%K 最优控制
%K 稳定性
%K 反问题
%K &lt
%K br&gt
%K optimal control
%K existence
%K uniqueness
%K inverse problem
%K stability
%K Kolmogorov equation
%U http://lxbwk.njournal.sdu.edu.cn/CN/10.6040/j.issn.1671-9352.0.2015.268