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Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation

Author

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  • Ruan, Zhousheng
  • Zhang, Wen
  • Wang, Zewen

Abstract

In this paper, a simultaneous identification problem of the spacewise source term and the fractional order for a time-fractional diffusion equation is considered. Firstly, under some assumption and with two different kinds of observation data for one-dimensional and two-dimensional time-fractional diffusion equation, the unique results of the inverse problem are proven by the Laplace transformation method and analytic continuation technique. Then the inverse problems are transformed into Tikhonov type optimization problems, the existence of optimal solutions to the Tikhonov functional is proven. Finally, we adopt an alternating minimization algorithm to solve the optimization problems. The efficiency and stability of the inversion algorithm are tested by several one- and two-dimensional examples.

Suggested Citation

  • Ruan, Zhousheng & Zhang, Wen & Wang, Zewen, 2018. "Simultaneous inversion of the fractional order and the space-dependent source term for the time-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 365-379.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:365-379
    DOI: 10.1016/j.amc.2018.01.025
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    Cited by:

    1. Mimi Li & Gongsheng Li & Zhiyuan Li & Xianzheng Jia, 2020. "Determination of Time-Dependent Coefficients in Time-Fractional Diffusion Equations by Variational Iteration Method," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(1), pages 1-74, February.
    2. Xian, Jun & Yan, Xiong-bin & Wei, Ting, 2020. "Simultaneous identification of three parameters in a time-fractional diffusion-wave equation by a part of boundary Cauchy data," Applied Mathematics and Computation, Elsevier, vol. 384(C).

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