一种反演抛物型方程未知系数的全变差正则化方法

A Total Variation Regularization Method for Identifying An Unknown Coefficient of A Parabolic Equation

基于最优控制理论框架,利用全变差正则化技巧,讨论了在终端观测值已知的前提下一种反演二阶抛物型方程未知系数的数值计算方法.结合对正问题的分析,推出了关于未知系数所满足的必要条件,并通过引入"磨光"全变差正则化项,反演了未知系数可能存在奇性的条件下的数值解.

Based on the optimal control framework,a numerical method for solving the unknown coefficient of the two order parabolic equation is discussed by using the total variation regularization method.Combining with the direct problem a necessary condition for the satisfaction of unkown coefficients is deduced.Through the introduction of a ＂polished＂total variation regularization term,the numerical solution of the unknown coefficients is reconstructed.