一类退化椭圆方程的耗散系数识别问题  

Identification Problem of Dissipation Coefficients for a Class of Degenerate Elliptic Equations

作　　者：张霁澳 杜润梅 ZHANG Ji'ao;DU Runmei(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,长春130012

出　　处：《吉林大学学报（理学版）》2024年第5期1037-1042,共6页Journal of Jilin University:Science Edition

基　　金：吉林省科技发展计划项目(批准号:20220101033JC)。

摘　　要：首先,考虑一类退化椭圆方程的耗散系数识别问题,通过把未知的耗散系数视为控制函数,把方程的解视为状态变量,定义目标泛函为状态与测量值的误差与人工正则项的和,将系数识别问题转化为最优控制问题.其次,利用最优控制问题的研究方法研究系数识别问题,给出最优控制的表达式,并证明在适当条件下最优控制的唯一性.Firstly,we considered the identification problem of the dissipation coefficients for a class of degenerate elliptic equations.By treating the unknown dissipation coefficients as control functions,treating the solutions of the equation as state variables,and defining the objective functional as the sum of the error between the state and the measurement values and the artificial regularization term,we transformed the coefficient identification problem into an optimal contro l problem.Secondly,the coefficient identification problem was studied by using the research method of the optimal control problem.We gave the expression of the optimal control and proved the uniqueness of optimal control under appropriate conditions.

关 键 词：退化椭圆方程 系数识别 最优控制 

分 类 号：O175.25[理学—数学]