MODIFIED QUASI-BOUNDARY VALUE METHOD FOR CAUCHY PROBLEMS OF ELLIPTIC EQUATIONS WITH VARIABLE COEFFICIENTS

被引：0

作者：

Zhang, Hongwu ^{[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：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年

关键词：

Ill-posed problem; Cauchy problem; elliptic equation; quasi-boundary value method; convergence estimates; ILL-POSED PROBLEMS; LAPLACE-EQUATION; REGULARIZATION; APPROXIMATION; STABILITY;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.

引用

页数：10

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