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Laplace方程Cauchy问题的Tikhonov正则化方法
引用本文:张宏武.Laplace方程Cauchy问题的Tikhonov正则化方法[J].佳木斯工学院学报,2009(1):132-133.
作者姓名:张宏武
作者单位:甘肃省河西学院数学系,甘肃张掖734000
摘    要:考虑了矩形区域上一个Laplace方程的Cauchy问题。对y=0时的Cauchy数据,以及x=0,x=π时的边界数据均已给出,要求0〈Y≤1时的解。对该不适定问题,文中用Tikhonov正则化方法构造正则化解,并证明了所得正则化解稳定地收敛于精确解。

关 键 词:不适定问题  Laplace方程  柯西问题  Tikhonov正则化方法

Tikhonov Regularization Method for the Cauchy Problem of the Laplace Equation
Affiliation:ZHANG Hong - wu (Hexi University Department of Mathematics, Zhangye 734000, China)
Abstract:In this paper, a Cauchy problem for the Laplace equation is considered in a rectangle domain. Cauchy data are given at y = 0 , and the boundary data are given at x = 0 and x = 7π . The solution for 0 〈 y ≤ 1 is sought. It is know that such problem is severely ill - posed. The authors use Tikhonov regularization. method to solve it. Convergence estimations are presented under an a - priori boundary assumption for the exact solution.
Keywords:Ill- posed problem  Laplace equation  Cauchy problem  Tikhonov regularization method
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