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Identification of source term in a nonlinear degenerate parabolic equation with memory

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Abstract

In this work, we consider an inverse backward problem for a nonlinear parabolic equation of the Burgers’ type with a memory term from final data. To this aim, we first establish the well-posedness of the direct problem. On the basis of the optimal control framework, the existence and necessary condition of the minimizer for the cost functional are established. The global uniqueness and stability of the minimizer are deduced from the necessary condition. Numerical experiments demonstrate the effectiveness of this approach.

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Authors and Affiliations

  1. Faculté des Sciences et Techniques, Université Hassan Premier, 50 Rue Ibnou Lhaytham, B.P. 577, Settat, 26002, Marocco

    Soufiane Abid, Khalid Atifi & El-Hassan Essoufi

  2. Faculté des sciences Dhar el Mahraz, Université Sidi Mohamed Ben Abdellah, Route d’Imouzzer, BP 2626, Fez, 30000, Marocco

    Abderrahim Zafrar

Authors
  1. Soufiane Abid
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  2. Khalid Atifi
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  3. El-Hassan Essoufi
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  4. Abderrahim Zafrar
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Correspondence to Soufiane Abid.

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Abid, S., Atifi, K., Essoufi, EH. et al. Identification of source term in a nonlinear degenerate parabolic equation with memory. Appl Math 69, 209–232 (2024). https://doi.org/10.21136/AM.2024.0049-23

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  • DOI: https://doi.org/10.21136/AM.2024.0049-23

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