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,未知系数是间断的函数.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.运用Gradient型迭代法进行数值模拟,且未知系数反演的效果也很好.
The inverse problem of determining the unknown coefficient from the final measurement data is discussed, which has important application in a large fields of applied science, and the radiative coefficient is a discontinuous function.Based on the optimal control framework, the existence, uniqueness and stability of the minimizer for the cost functional are established, the numerical simulation with the Gradient iterative method is conducted, and that the unknown coefficient is recovered very well.
作者
曾剑
张泰年
任建龙
甄苇苇
Zeng Jian;Zhang Tainian;Ren Jianlong;ZhenWeiwei(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
2019年第3期208-214,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
唯一性
稳定性
数值模拟
inverse problem
optimal control
uniqueness
stability
numerical simulation
