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Determination of Initial Distribution for a Space-Fractional Diffusion Equation with Time-Dependent Diffusivity

Bulletin of the Malaysian Mathematical Sciences Society volume 44, pages 3461–3487 (2021)Cite this article

Abstract

In the present paper, we devote our aspiration to some initial and final value problems for a class of space-fractional diffusion equation with time-dependent diffusivity factor. For the initial value problem (IVP), we investigate the stability of the solution concerning the data and the fractional order. For the final value problem, we prove the ill-posedness and suggest a filter method to regularize the problem. Explicit convergence rate of Hölder type is established. Finally, several numerical examples based on the finite difference approximation and the discrete Fourier transform are performed to demonstrate the effectiveness of the proposed method.

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Authors and Affiliations

  1. Institute for Computational Science and Technology, Ho Chi Minh City, Vietnam

    Tran Nhat Luan

  2. Division of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tra Quoc Khanh

  3. Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam

    Tra Quoc Khanh

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  1. Tran Nhat Luan
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  2. Tra Quoc Khanh
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Luan, T.N., Khanh, T.Q. Determination of Initial Distribution for a Space-Fractional Diffusion Equation with Time-Dependent Diffusivity. Bull. Malays. Math. Sci. Soc. 44, 3461–3487 (2021). https://doi.org/10.1007/s40840-021-01118-7

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  • DOI: https://doi.org/10.1007/s40840-021-01118-7

Keywords

  • Space-fractional diffusion equation
  • Ill-posed problem
  • Filter regularization
  • Lipschitz continuity

Mathematics Subject Classification

  • 65N20
  • 35R25
  • 47J06
  • 26A33