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An Inverse Problem for a Two-Dimensional Time-Fractional Sideways Heat Equation

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  • Songshu Liu
  • Lixin Feng

Abstract

In this paper, we consider a two-dimensional (2D) time-fractional inverse diffusion problem which is severely ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. A modified kernel method is presented for approximating the solution of this problem, and the convergence estimates are obtained based on both a priori choice and a posteriori choice of regularization parameters. The numerical examples illustrate the behavior of the proposed method.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlmpe:5865971
    DOI: 10.1155/2020/5865971
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    Cited by:

    1. 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.
    2. Rafał Brociek & Agata Wajda & Damian Słota, 2021. "Inverse Problem for a Two-Dimensional Anomalous Diffusion Equation with a Fractional Derivative of the Riemann–Liouville Type," Energies, MDPI, vol. 14(11), pages 1-17, May.
    3. Slawomir Blasiak, 2021. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach," Energies, MDPI, vol. 14(17), pages 1-13, September.

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