Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation

A Cauchy problem for the semi-linear elliptic equation is investigated. We use a filtering function method to define a regularization solution for this ill-posed problem. The existence, uniqueness and stability of the regularization solution are proven; a convergence estimate of Hölder type for the regularization method is obtained under the a-priori bound assumption for the exact solution. An iterative scheme is proposed to calculate the regularization solution; some numerical results show that this method works well.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Zhang, H. and Zhang, X. (2015) Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation. Journal of Applied Mathematics and Physics, 3, 1599-1609. doi: 10.4236/jamp.2015.312184.

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