非散度型椭圆方程系数识别问题的正则化解

Convergence Rates of Regularization Solution forCoefficient Identification Problems in Elliptic Equation

研究了非散度型椭圆方程系数识别问题Tikhonov正则化解的收敛速度.由于反问题是不适定的,利用Tikhonov正则化方法将原问题转化为最优化问题,并构造相应的泛函.相较于散度型方程,这里的困难有两方面:①非散度型算子不利于分部积分;②控制泛函可能没有凸性.基于正问题的先验估计以及附加的源条件,获得了正则化解的收敛速度.

This paper mainly studies the convergence rate of Tikhonov regularization solution for coefficient identification in nondivergent elliptic equation.Since the inverse problem is ill-posed,the Tikhonov regularization method is used to transform the original problem into an optimization problem,and construct the corresponding functional.Compared to divergence equation,there are two difficulties:the non-divergent operator is not conducive to partial integration,and the control functional may lack convexity.Based on the prior estimation of the forward problem and additional source conditions,the convergence rate of regularized solution is obtained.