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Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation

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  • Yonggang Chen

    (College of Science, China University of Petroleun East China, Qingdao 257099, China)

  • Yu Qiao

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

  • Xiangtuan Xiong

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

Abstract

The inverse and ill-posed problem of determining a solute concentration for the two-dimensional nonhomogeneous fractional diffusion equation is investigated. This model is much worse than its homogeneous counterpart as the source term appears. We propose a modified kernel regularization technique for the stable numerical reconstruction of the solution. The convergence estimates under both a priori and a posteriori parameter choice rules are proven.

Suggested Citation

  • Yonggang Chen & Yu Qiao & Xiangtuan Xiong, 2022. "Regularization Error Analysis for a Sideways Problem of the 2D Nonhomogeneous Time-Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:10:p:1742-:d:819184
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    References listed on IDEAS

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    1. Raberto, Marco & Scalas, Enrico & Mainardi, Francesco, 2002. "Waiting-times and returns in high-frequency financial data: an empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 749-755.
    2. Songshu Liu & Lixin Feng, 2020. "An Inverse Problem for a Two-Dimensional Time-Fractional Sideways Heat Equation," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, March.
    3. Li, Changpin & Wang, Zhen, 2020. "The discontinuous Galerkin finite element method for Caputo-type nonlinear conservation law," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 169(C), pages 51-73.
    4. Songshu Liu & Lixin Feng, 2018. "A Revised Tikhonov Regularization Method for a Cauchy Problem of Two-Dimensional Heat Conduction Equation," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, May.
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