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The Truncation Regularization Method for Identifying the Initial Value on Non-Homogeneous Time-Fractional Diffusion-Wave Equations

Author

Listed:
  • Fan Yang

    (Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China)

  • Qu Pu

    (Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China)

  • Xiao-Xiao Li

    (Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China)

  • Dun-Gang Li

    (Department of Applied Mathematics, School of Science, Lanzhou University of Technology, Lanzhou, Gansu 730050, China)

Abstract

In the essay, we consider an initial value question for a mixed initial-boundary value of time-fractional diffusion-wave equations. This matter is an ill-posed problem; the solution relies discontinuously on the measured information. The truncation regularization technique is used for restoring the initial value functions. The convergence estimations are given in a priori regularization parameter choice regulations and a posteriori regularization parameter choice regulations. Numerical examples are given to demonstrate this is effective and practicable.

Suggested Citation

  • Fan Yang & Qu Pu & Xiao-Xiao Li & Dun-Gang Li, 2019. "The Truncation Regularization Method for Identifying the Initial Value on Non-Homogeneous Time-Fractional Diffusion-Wave Equations," Mathematics, MDPI, vol. 7(11), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1007-:d:279635
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    References listed on IDEAS

    as
    1. Balescu, R., 2007. "V-Langevin equations, continuous time random walks and fractional diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 62-80.
    2. Fan Yang & Ping Fan & Xiao-Xiao Li & Xin-Yi Ma, 2019. "Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source," Mathematics, MDPI, vol. 7(9), pages 1-13, September.
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