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A mollifier approach to the simultaneous identification of the unknown source and initial distribution in a space-fractional diffusion equation

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  • Qiao, Yu
  • Xiong, Xiangtuan

Abstract

In this paper, a simultaneous inversion problem for the Riesz-Feller space-fractional diffusion equation with inexact operators is investigated, which is to identify the source term and initial value from two over-specified measurements. The problem model is well known to be ill-posed. We propose a regularization method to deal with the inverse problem using the idea of mollification. Under an a priori and an a posteriori parameter choice rules, we derive explicit error estimates between the exact solutions and their regularized approximations in the practical case where both the operators and the data are noisy. Numerical results show that the proposed method is efficient, and the unknown terms are recovered quite well.

Suggested Citation

  • Qiao, Yu & Xiong, Xiangtuan, 2025. "A mollifier approach to the simultaneous identification of the unknown source and initial distribution in a space-fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 489(C).
    • Handle: RePEc:eee:apmaco:v:489:y:2025:i:c:s0096300324006362
    DOI: 10.1016/j.amc.2024.129175
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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. Hohage, Thorsten & Maréchal, Pierre & Simar, Léopold & Vanhems, Anne, 2024. "A Mollifier Approach To The Deconvolution Of Probability Densities," Econometric Theory, Cambridge University Press, vol. 40(2), pages 320-359, April.
    3. Zhang, Z.Q. & Wei, T., 2013. "An optimal regularization method for space-fractional backward diffusion problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 92(C), pages 14-27.
    4. Simo Tao Lee, Walter C., 2023. "A variational technique of mollification applied to backward heat conduction problems," Applied Mathematics and Computation, Elsevier, vol. 449(C).
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