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

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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.

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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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