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Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis

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  • Joelma Azevedo
  • Claudio Cuevas
  • Erwin Henriquez

Abstract

One of the most important systems for understanding chemotactic aggregation is the Keller–Segel system. We consider the time‐fractional Keller–Segel system of order α∈(0,1). We prove an existence result with small initial data in a class of Besov–Morrey spaces. Self‐similar solutions are obtained and we also show an asymptotic behaviour result.

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  • Joelma Azevedo & Claudio Cuevas & Erwin Henriquez, 2019. "Existence and asymptotic behaviour for the time‐fractional Keller–Segel model for chemotaxis," Mathematische Nachrichten, Wiley Blackwell, vol. 292(3), pages 462-480, March.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:3:p:462-480
    DOI: 10.1002/mana.201700237
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    Cited by:

    1. Caicedo, Alejandro & Cuevas, Claudio & Mateus, Éder & Viana, Arlúcio, 2021. "Global solutions for a strongly coupled fractional reaction-diffusion system in Marcinkiewicz spaces," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Guo, Liujie & Gao, Fei & Zhan, Hui, 2022. "Existence, uniqueness and L∞-bound for weak solutions of a time fractional Keller-Segel system," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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