Modified quasi-boundary value method for a Cauchy problem of semi-linear elliptic equation

被引：10
|
作者：
Zhang, H. W. [1 ,2 ]
机构：
[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Gansu, Peoples R China
[2] Hexi Univ, Sch Math & Stat, Zhangye City 734000, Gansu, Peoples R China
来源：
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2012年 / 89卷 / 12期
关键词：
ill-posed problem; Cauchy problem; semi-linear elliptic equation; modified quasi-boundary value method; convergence estimate;
D O I：
10.1080/00207160.2012.693174
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate a Cauchy problem for the semi-linear elliptic equation. This problem is well known to be severely ill-posed and regularization methods are required. We use a modified quasi-boundary value method to deal with it, and a convergence estimate for the regularized solution is obtained under an a priori bound assumption for the exact solution. Finally, some numerical results show that our given method works well.
引用
收藏
页码：1689 / 1703
页数：15
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