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Well‐posedness and blow‐up of the fractional Keller–Segel model on domains

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  • Masterson Costa
  • Claudio Cuevas
  • Clessius Silva
  • Herme Soto

Abstract

This work deals with well‐posedness and blow‐up in the setting of Lebesgue and Besov spaces to the time‐fractional Keller–Segel model for chemotaxis under homogeneous Neumann boundary conditions in a smooth domain of RN$\mathbb {R}^N$. The KS model consists in a coupled system of partial differential equations. In particular, we also treat the unique continuation of the solution and the persistence of continuous dependence on the initial data for the continued solution.

Suggested Citation

  • Masterson Costa & Claudio Cuevas & Clessius Silva & Herme Soto, 2023. "Well‐posedness and blow‐up of the fractional Keller–Segel model on domains," Mathematische Nachrichten, Wiley Blackwell, vol. 296(12), pages 5569-5592, December.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:12:p:5569-5592
    DOI: 10.1002/mana.202200235
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    References listed on IDEAS

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    1. Haobin Liu & Hassan Khan & Rasool Shah & A. A. Alderremy & Shaban Aly & Dumitru Baleanu, 2020. "On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions," Complexity, Hindawi, vol. 2020, pages 1-15, July.
    2. Atangana, Abdon & Alqahtani, Rubayyi T., 2018. "New numerical method and application to Keller-Segel model with fractional order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 14-21.
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