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Inverse Problem of Identifying a Time-Dependent Source Term in a Fractional Degenerate Semi-Linear Parabolic Equation

Author

Listed:
  • Maroua Nouar

    (Departement of Mathematics, Abbes Laghrour University Khenchela, Khenchela 40004, Algeria)

  • Chattouh Abdeledjalil

    (Departement of Mathematics, Abbes Laghrour University Khenchela, Khenchela 40004, Algeria)

  • Omar Mossa Alsalhi

    (Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca 21961, Saudi Arabia)

  • Hamed Ould Sidi

    (Département des Méthodes Quantitatives et Informatiques, Institut Supérieur de Comptabilité et d’Administration des Entreprises (ISCAE), Nouakchott 6093, Mauritania)

Abstract

This work investigates the inverse problem of identifying a time-dependent source term in a time-fractional semi-linear degenerate parabolic equation using integral measurement data. We establish the unique solvability of the inverse problem within a suitable functional framework. The proof methodology is based on the Rothe method, where the variational formulation is discretized in time, and a priori estimates for discrete solutions are derived. These estimates are then utilized to demonstrate the convergence of Rothe approximations to a unique weak solution. Additionally, we develop a numerical scheme based on the L 1 -Galerkin finite element method, combined with iterative refinement, to reconstruct the unknown source term. The numerical performance of the proposed method is validated through a series of computational experiments, demonstrating its stability and robustness against noisy data.

Suggested Citation

  • Maroua Nouar & Chattouh Abdeledjalil & Omar Mossa Alsalhi & Hamed Ould Sidi, 2025. "Inverse Problem of Identifying a Time-Dependent Source Term in a Fractional Degenerate Semi-Linear Parabolic Equation," Mathematics, MDPI, vol. 13(9), pages 1-25, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:9:p:1486-:d:1646835
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