椭圆型方程系数识别问题正则化解的收敛速度

Convergence Rates of Regularization Solutions for Coefficient Identification Problems in Elliptic Equation

研究了椭圆型方程系数识别问题Tikhonov正则化解的收敛速度。由于反问题是不适定的,用Tikhonov正则化方法将原问题转化为最优化问题。构造从系数到解的映射,利用解的观测值和先验估计,建立相应的极小化严格凸泛函,进一步证明泛函在容许集内有唯一的全局极小值,通过附加简单的源条件,获得正则化解的收敛速度。

This paper studies the convergence rate of Tikhonov regularization solutions for coefficient recognition of elliptic equations.Since the inverse problem wasill-posed,the Tikhonov regulation method has been used to transform the original problem into the optimization one.In the paper,a mapping from coefficients to solutions is constructed.By using the observed values and prior estimates of solutions,the corresponding minimization strictly convex functional is established.It is further proved that the functional has a unique global minimum in the admissible set.By adding simple source conditions,the convergence rate of the regularized solution is obtained.