In this article, we study a Cauchy problem for an elliptic equation with variable coefficients. It is well-known that such a problem is severely ill-posed; i.e., the solution does not depend continuously on the Cauchy data. We propose a modified quasi-boundary value regularization method to solve it. Convergence estimates are established under two a priori assumptions on the exact solution. A numerical example is given to illustrate our proposed method.
Submitted May 4, 2011. Published August 23, 2011.
Math Subject Classifications: 35J15, 35J57, 65G20, 65T50.
Key Words: Ill-posed problem; Cauchy problem; elliptic equation; quasi-boundary value method; convergence estimates.
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| Hongwu Zhang |
School of Mathematics and Statistics, Lanzhou University
Lanzhou city, Gansu Province, 730000, China
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