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Existence, uniqueness and L∞-bound for weak solutions of a time fractional Keller-Segel system

Author

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  • Guo, Liujie
  • Gao, Fei
  • Zhan, Hui

Abstract

We study the global existence, uniqueness and L∞-bound for the weak solutions to a time fractional Keller-Segel systems with logistic source∂αu∂tα=Δu−∇⋅u∇v+ua−bu,x∈ℝn,t>00=Δv+u,x∈ℝn,t>0

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003952
    DOI: 10.1016/j.chaos.2022.112185
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    References listed on IDEAS

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    1. Mimura, Masayasu & Tsujikawa, Tohru, 1996. "Aggregating pattern dynamics in a chemotaxis model including growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 230(3), pages 499-543.
    2. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    3. 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.
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