A mollification regularization method for the Cauchy problem of an elliptic equation in a multi-dimensional case

被引：21

作者：

Cheng, Hao ^{[1
]}

Feng, Xiao-Li ^{[1
]}

Fu, Chu-Li ^{[1
]}

机构：

[1] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China

来源：

INVERSE PROBLEMS IN SCIENCE AND ENGINEERING | 2010年 / 18卷 / 07期

关键词：

Cauchy problem of an elliptic equation; ill-posed problem; mollification method; error estimates; LAPLACE-EQUATION;

D O I：

10.1080/17415977.2010.492519

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this article, we consider a Cauchy problem of an elliptic equation in a multidimensional case. This problem is severely ill-posed: the solution (if it exists) does not depend continuously on the data. To deal with this problem, we propose a mollification method. Error estimates show that the regularized solution depends continuously on the data. Numerical examples verify that the proposed regularization strategy is effective and numerical calculation is stable in the multi-dimensional case.

引用

页码：971 / 982

页数：12

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