Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 106, pp. 110.
Modified quasiboundary value method for Cauchy problems
of elliptic equations with variable coefficients
Hongwu Zhang
Abstract:
In this article, we study a Cauchy problem for an elliptic
equation with variable coefficients. It is wellknown that such a
problem is severely illposed; i.e., the solution does not depend
continuously on the Cauchy data. We propose a modified quasiboundary
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: Illposed problem; Cauchy problem; elliptic equation;
quasiboundary value method; convergence estimates.
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Hongwu Zhang
School of Mathematics and Statistics, Lanzhou University
Lanzhou city, Gansu Province, 730000, China
email: zhhongwu@163.com

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