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Identifying a diffusion coefficient in a time-fractional diffusion equation

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  • Wei, T.
  • Li, Y.S.

Abstract

In this paper, we propose a conjugate gradient algorithm for identifying a space-dependent diffusion coefficient in a time-fractional diffusion equation from the boundary Cauchy data in one-dimensional case. The existence and uniqueness of the solution for a weak form of the direct problem are obtained. The identification of diffusion coefficient is formulated into a variational problem by the Tikhonov-type regularization. The existence, stability and convergence of a minimizer for the variational problem approach to the exact diffusion coefficient are provided. We use a conjugate gradient method to solve the variational problem based on the deductions of a sensitive problem and an adjoint problem. We test three numerical examples and show the effectiveness of the proposed method.

Suggested Citation

  • Wei, T. & Li, Y.S., 2018. "Identifying a diffusion coefficient in a time-fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 151(C), pages 77-95.
    • Handle: RePEc:eee:matcom:v:151:y:2018:i:c:p:77-95
    DOI: 10.1016/j.matcom.2018.03.006
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    References listed on IDEAS

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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
    2. Giona, Massimiliano & Cerbelli, Stefano & Roman, H.Eduardo, 1992. "Fractional diffusion equation and relaxation in complex viscoelastic materials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 449-453.
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    Cited by:

    1. Liu, Jun & Fu, Hongfei & Zhang, Jiansong, 2020. "A QSC method for fractional subdiffusion equations with fractional boundary conditions and its application in parameters identification," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 153-174.

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