Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation  

作　　者：Hongwu Zhang Xiaoju Zhang 

机构地区：[1]School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, China

出　　处：《Journal of Applied Mathematics and Physics》2015年第12期1599-1609,共11页应用数学与应用物理（英文）

摘　　要：A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven;a convergence estimate of H?lder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution;some numerical results show that this method works well.A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven;a convergence estimate of H?lder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution;some numerical results show that this method works well.

关 键 词：ILL-POSED PROBLEM CAUCHY PROBLEM SEMI-LINEAR Elliptic Equation FILTERING Function Method Convergence Estimate 

分 类 号：O1[理学—数学]