TITLE:
Filtering Function Method for the Cauchy Problem of a Semi-Linear Elliptic Equation
AUTHORS:
Hongwu Zhang, Xiaoju Zhang
KEYWORDS:
Ill-Posed Problem, Cauchy Problem, Semi-Linear Elliptic Equation, Filtering Function Method, Convergence Estimate
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.12,
December
17,
2015
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.