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J. R. Cannon, “The One-Dimensional Heat Equation,” Addison-Wesley Publishing Company, Menlo Park, 1984.

has been cited by the following article:

• TITLE: Quasi-Reversibility Regularization Method for Solving a Backward Heat Conduction Problem

  AUTHORS: Ailin Qian, Jianfeng Mao

  KEYWORDS: Back Heat Conduction, Ill-Posed Problem, Quasi-Reversibility, Regularization

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.3, September 19, 2011

  ABSTRACT: Non-standard backward heat conduction problem is ill-posed in the sense that the solution(if it exists) does not depend continuously on the data. In this paper, we propose a regularization strategy-quasi-reversibility method to analysis the stability of the problem. Meanwhile, we investigate the roles of regularization parameter in this method. Numerical result show that our algorithm is effective and stable.