Acta mathematica scientia,Series A ›› 2020, Vol. 40 ›› Issue (3): 717-724.

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A Super Order Regularization Method for Determination of an Unknown Source in the Heat Equation

Zhenyu Zhao1,2,3,*(),Riguang Lin2,Zhi Li2,Duan Mei2   

  1. 1 School of Mathematics and Statistics, Shandong University of Technology, Shandong Zibo 255049
    2 Faculty of Mathematics and Computer Science, Guangdong Ocean University, Guangdong Zhanjiang 524088
    3 Southern Marine Science and Engineering Guangdong Laboratory(Zhanjiang), Guangdong Zhanjiang 524088
  • Received:2019-02-18 Online:2020-06-26 Published:2020-07-15
  • Contact: Zhenyu Zhao E-mail:wozitianshanglai@163.com
  • Supported by:
    the Fund of Southern Marine Science and Engineering Guangdong Laboratory (Zhanjiang)(ZJW-2019-04);the Project of Enhancing School with Innovation of Guangdong Ocean University(Q18306)

Abstract:

The problem for determining an unknown source in the heat equation is considered in this paper. We present a Tikhonov regularization method with a super order penalty term to deal with illposedness of the problem. The regularization parameter is chosen by a discrepancy principle and the order optimal error bounds can be obtained for various smooth conditions. The smoothness parameter and the a priori bound of exact solution are not needed in the numerical process. Numerical tests show that the proposed method is effective and stable.

Key words: Ill-posed problem, Super order regularization, Heat equation, Unknown source, Discrepancy principle

CLC Number: 

  • O124
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