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Two regularization methods for a Cauchy problem for the Laplace equation
Authors:Zhi Qian  Chu-Li Fu  Zhen-Ping Li
Affiliation:School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, People's Republic of China
Abstract:A Cauchy problem for the Laplace equation in a rectangle is considered. Cauchy data are given for y=0, and boundary data are for x=0 and x=π. The solution for 0<y?1 is sought. We propose two different regularization methods on the ill-posed problem based on separation of variables. Both methods are applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates.
Keywords:Ill-posed problem   Cauchy problem for Laplace equation   Regularization
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