椭圆方程Cauchy问题的小波正则化方法（英文）

Wavelet regularization method for a Cauchy problem of an elliptic equation

考虑平行于x轴的带状区域上具有约束条件的椭圆方程的Cauchy问题。此问题是不稳定的,小波正则化方法可以用来稳定地求解此问题,其关键是利用正交的MRA,选择适当的磨光化参数将Cauchy数据磨光,其中MRA是基于Meyer小波形成的。同时得到相应正则解Hlder形式的稳定性估计。数值实验表明,该方法是有效的。

Consider a Cauchy problem of an elliptic equation in a strip parallel to the x-axis under certain constraint.Due to the character of instability,the wavelet regularization method is applied to solve the problem in a stable way.The key technique is to mollify the Cauchy data by the means of orthogonal multiresolution analysis-based Meyer wavelets with appropriate choice of mollification parameters.Some stability estimates of Hlder type for the regularized solution are obtained.Numerical examples are given which show the efficiency of this method.