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On a quasi-reversibility regularization method for a Cauchy problem of the Helmholtz equation |
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| Authors: | Ai-Lin Qian Xiang-Tuan Xiong |
| Affiliation: | a Department of Mathematics, Lanzhou University, Lanzhou, Gansu, 730000, People’s Republic of China b Department of Mathematics, Northwest Normal University, Lanzhou, Gansu, 730070, People’s Republic of China c Department of Mathematics and Statistics, Xianning University, Xianning, Hubei, 437000, People’s Republic of China |
| Abstract: | In this paper, we consider the Cauchy problem for the Helmholtz equation in a rectangle, where the Cauchy data is given for y=0 and boundary data are for x=0 and x=π. The solution is sought in the interval 0<y≤1. A quasi-reversibility method is applied to formulate regularized solutions which are stably convergent to the exact one with explicit error estimates. |
| Keywords: | Ill-posed Cauchy problem of Helmholtz equation Quasi-reversibility Regularization |
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