Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 106, pp. 1-10.
Title: Modified quasi-boundary value method for Cauchy problems
of elliptic equations with variable coefficients
Author: Hongwu Zhang (Lanzhou Univ., Gansu, China)
Abstract:
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.