摘要
讨论了一个利用终端观测数据重构抛物型方程未知系数的反问题,这类问题在一些科学研究中有重要的应用.与一般问题不同的是,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,证明了控制泛函极小元的存在性及其满足的必要条件,并讨论了最优解的唯一性及稳定性.在正问题的计算中,建立了离散的有限差分格式并运用追赶法求原方程的数值解.
The inverse problem of determining the unknown coefficient in parabolic equations from the final measurement data is discussed.Problems of this type have important applications in many fields of applied science and engineering.Being different from other general inverse coefficient problems,the unknown coefficient depends on both the space variable xand the time t.Based on the optimal control framework,the existence and the necessary conditions which must be satisfied by the minimizer are proved.Then the uniqueness and stability of the minimizer for the cost functional are also established.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.
作者
任建龙
曾剑
甄苇苇
Ren Jianlong;Zeng Jian;Zhen Weiwei(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《宁夏大学学报（自然科学版）》
CAS
2018年第2期97-103,共7页
Journal of Ningxia University(Natural Science Edition)
基金
国家自然科学基金资助项目(11261029
11461039)
甘肃省自然科学基金资助项目(145RJZA124)
关键词
反问题
最优控制
存在性
唯一性
稳定性
差分格式
inverse problem
optimal control
existence
uniqueness
stability
difference scheme
