一类带积分型源项的对流-扩散方程的初值反演问题  

Initial Value Inverse Problem of a Convection-DiffusionEquation with Integral Source Term

作　　者：钱坤 镡锐霞 丰利香 QIAN Kun;TAN Ruixia;FENG Lixiang(Ningxia Institute of Science and Technology,School of Science and Chemical Engineering,Shizuishan 753000,Ningxia China)

机构地区：[1]宁夏理工学院理学与化学工程学院,宁夏石嘴山753000

出　　处：《吉首大学学报（自然科学版）》2024年第5期11-16,共6页Journal of Jishou University(Natural Sciences Edition)

基　　金：宁夏回族自治区自然科学基金资助项目(2021AAC03256)。

摘　　要：主要讨论了一类带有积分型源项的对流-扩散方程的初值反演问题.在最优化控制理论框架下,证明了控制泛函最优解的存在性,得到了最优解满足的必要条件.利用必要条件,通过一些正问题的先验估计证明了最优解具有非局部唯一性和稳定性.This paper mainly discusses the initial value inverse problem of a convection-diffusion equation with integral source term.Based on the optimal control framework,the existence of the optimal solution for the control functional is proved,and the necessary condition for the optimal solution is deduced.Finally,with the necessary conditions,non-local uniqueness and stability of the optimal solution are proved by the prior estimates of the forward problem.

关 键 词：积分型源项 反问题 最优化控制 唯一性 稳定性 

分 类 号：O175.26[理学—数学]