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Lavrentiev, M.M., Romanov, V.G. and Shishatski, S.P. (1986) Ill-Posed Problems of Mathematical Physics and Analysis. Translations of Mathematical Monographs, Vol. 64, American Mathematical Society, Providence.

has been cited by the following article:

• 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.