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Inverse source problems for identifying time and space-dependent coefficients in a 2D generalized diffusion equation

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  • Ilyas, Asim
  • Serra-Capizzano, Stefano

Abstract

This article addresses two inverse source problems related to determining a space-dependent source term and a time-dependent coefficient in a two-dimensional generalized diffusion equation. The considered problems are ill-posed in the Hadamard sense, where small perturbations in the data can lead to uncontrolled variations in the solution. The present work also provides existence and uniqueness results for the solutions of these problems under appropriate over-specified and regularity conditions. Special cases of the diffusion equation are examined, focusing on specific selections of the memory kernel involved in the time-fractional derivative. The results are illustrated with several examples, demonstrating the practical implications of the proposed methods for inverse source problems.

Suggested Citation

  • Ilyas, Asim & Serra-Capizzano, Stefano, 2025. "Inverse source problems for identifying time and space-dependent coefficients in a 2D generalized diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    • Handle: RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325003236
    DOI: 10.1016/j.amc.2025.129597
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    References listed on IDEAS

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    1. Yuriy Povstenko, 2015. "Linear Fractional Diffusion-Wave Equation for Scientists and Engineers," Springer Books, Springer, edition 127, number 978-3-319-17954-4, October.
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    3. Ilyas, Asim & Malik, Salman A. & Saif, Summaya, 2023. "Recovering Source Term and Temperature Distribution for Nonlocal Heat Equation," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    4. Sandev, Trifce & Sokolov, Igor M. & Metzler, Ralf & Chechkin, Aleksei, 2017. "Beyond monofractional kinetics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 210-217.
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