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

Hongwu Zhang, Xiaoju Zhang

School of Mathematics and Information Science, Beifang University of Nationalities, Yinchuan, China.

DOI: 10.4236/jamp.2015.312184                

Abstract

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.

Keywords

Ill-Posed Problem, Cauchy Problem, Semi-Linear Elliptic Equation, Filtering Function Method, Convergence Estimate

Conflicts of Interest

The authors declare no conflicts of interest.

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