The a posteriori Fourier method for solving the Cauchy problem for the Laplace equation with nonhomogeneous Neumann data |
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Authors: | Chu-Li Fu Yun-Jie Ma Hao Cheng Yuan-Xiang Zhang |
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Institution: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, PR China;2. School of Mathematics and Informational Science, Yantai University, Yantai, Shandong 264005, PR China;3. School of Science, Jiangnan University, Wuxi 214122, Jiangsu Province, PR China |
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Abstract: | In the present paper, the Cauchy problem for the Laplace equation with nonhomogeneous Neumann data in an infinite “strip” domain is considered. This problem is severely ill-posed, i.e., the solution does not depend continuously on the data. A conditional stability result is given. A new a posteriori Fourier method for solving this problem is proposed. The corresponding error estimate between the exact solution and its regularization approximate solution is also proved. Numerical examples show the effectiveness of the method and the comparison of numerical effect between the a posteriori and the a priori Fourier method are also taken into account. |
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Keywords: | Cauchy problem for the Laplace equation Ill-posed problem Conditional stability Regularization |
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