Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (2): 427-450.

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Fractional Landweber Iterative Regularization Method to Identify Source Term for the Rayleigh-Stokes Equation

Fan Yang*(),Qianchao Wang(),Xiaoxiao Li   

  1. School of Science, Lanzhou University of Technology, Lanzhou 730050
  • Received:2020-03-03 Online:2021-04-26 Published:2021-04-29
  • Contact: Fan Yang E-mail:yfggd114@163.com;wqcfaf@163.com
  • Supported by:
    the NSFC(11961044);the Dr Fund of Lanzhou University of Science and Technology

Abstract:

In this paper, the inverse problem of identifying the unknown sources for the Rayleigh-Stokes equation with a Riemann-Liouville fractional derivative in time is considered. We prove that such a problem is ill-posed and apply the fractional Landweber method to solve this inverse problem. Based on the results of conditional stability, under the priori and posteriori regularization parameters choice rules, the error estimates between the exact solution and the regularization solution are given respectively. Finally, several numerical examples are given to illustrate the effectiveness and feasibility of these methods.

Key words: Rayleigh-Stokes equation, Inverse problem, Identifying unknown source problem, Fractional Landweber iterative regularization method

CLC Number: 

  • O175
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