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Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis

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Abstract

In two space dimensions, the parabolic–parabolic Keller–Segel system shares many properties with the parabolic–elliptic Keller–Segel system. In particular, solutions globally exist in both cases as long as their mass is less than a critical threshold M c . However, this threshold is not as clear in the parabolic–parabolic case as it is in the parabolic–elliptic case, in which solutions with mass above M c always blow up. Here we study forward self-similar solutions of the parabolic–parabolic Keller–Segel system and prove that, in some cases, such solutions globally exist even if their total mass is above M c , which is forbidden in the parabolic–elliptic case.

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Authors and Affiliations

  1. Instytut Matematyczny, Uniwersytet Wrocławski, pl.Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Piotr Biler

  2. Département de Mathématiques, Université d’Évry Val d’Essonne, rue du père Jarlan, 91025, Évry Cédex, France

    Lucilla Corrias

  3. Ceremade (UMR CNRS 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775, Paris Cédex 16, France

    Jean Dolbeault

Authors
  1. Piotr Biler
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  2. Lucilla Corrias
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  3. Jean Dolbeault
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Corresponding author

Correspondence to Lucilla Corrias.

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Biler, P., Corrias, L. & Dolbeault, J. Large mass self-similar solutions of the parabolic–parabolic Keller–Segel model of chemotaxis. J. Math. Biol. 63, 1–32 (2011). https://doi.org/10.1007/s00285-010-0357-5

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  • DOI: https://doi.org/10.1007/s00285-010-0357-5

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