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Local criteria for blowup in two-dimensional chemotaxis models

  • Author Bio: E-mail address: Piotr.Biler@math.uni.wroc.pl; E-mail address: T.Cieslak@impan.pl; E-mail address: Grzegorz.Karch@math.uni.wroc.pl; E-mail address: Jacek.Zienkiewicz@math.uni.wroc.pl
  • * Corresponding author: Piotr Biler

    * Corresponding author: Piotr Biler 
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  • We consider two-dimensional versions of the Keller-Segel model for the chemotaxis with either classical (Brownian) or fractional (anomalous) diffusion. Criteria for blowup of solutions in terms of suitable Morrey spaces norms are derived. Moreover, the impact of the consumption term on the global-in-time existence of solutions is analyzed for the classical Keller-Segel system.

    Mathematics Subject Classification: Primary:35Q92;Secondary:35B44, 35K55.


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