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Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation

Author

Listed:
  • Chenyu Zhang

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

  • Fan Yang

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

  • Xiaoxiao Li

    (School of Science, Lanzhou University of Technology, Lanzhou 730050, China)

Abstract

In this paper, we delve into the challenge of identifying an unknown source in a space-time fractional diffusion-wave equation. Through an analysis of the exact solution, it becomes evident that the problem is ill-posed. To address this, we employ both the Tikhonov regularization method and the Quasi-boundary regularization method, aiming to restore the stability of the solution. By adhering to both a priori and a posteriori regularization parameter choice rules, we derive error estimates that quantify the discrepancies between the regularization solutions and the exact solution. Finally, we present numerical examples to illustrate the effectiveness and stability of the proposed methods.

Suggested Citation

  • Chenyu Zhang & Fan Yang & Xiaoxiao Li, 2024. "Two Regularization Methods for Identifying the Spatial Source Term Problem for a Space-Time Fractional Diffusion-Wave Equation," Mathematics, MDPI, vol. 12(2), pages 1-28, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:231-:d:1316788
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