Laplace方程Cauchy问题的Tikhonov正则化方法 |
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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. |
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作者姓名: | 张宏武 |
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作者单位: | 甘肃省河西学院数学系,甘肃张掖734000 |
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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。
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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 |
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Affiliation: | ZHANG Hong - wu (Hexi University Department of Mathematics, Zhangye 734000, China) |
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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. |
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Keywords: | Ill- posed problem Laplace equation Cauchy problem Tikhonov regularization method |
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