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A Global Existence Result for a Keller-Segel Type System With Supercritical Initial Data

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Abstract

We consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in time for general subcritical (ǁρ0ǁ1 < 8π) initial data, or blow—up in finite time for suitably chosen supercritical (ǁρ0ǁ1 > 8π) initial data with concentration around finitely many points. As a matter of fact there are no results claiming the existence of global solutions in the supercritical case. We solve this problem here and prove that, for a particular set of initial data which share large supercritical masses, the corresponding solution is global and uniformly bounded.

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Authors and Affiliations

  1. Department of Mathematics, University of Rome ”Tor Vergata”, Via della ricerca scientifica n.1, 00133, Roma, Italy

    Daniele Bartolucci

  2. Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121, Padova, Italy

    Daniele Castorina

Authors
  1. Daniele Bartolucci
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  2. Daniele Castorina
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Correspondence to Daniele Bartolucci.

Additional information

Research partially supported by FIRB project Analysis and Beyond and by MIUR project Metodi variazionali e PDE non lineari.

Research partially supported by project Bando Giovani Studiosi 2013 - Università di Padova - GRIC131695.

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Bartolucci, D., Castorina, D. A Global Existence Result for a Keller-Segel Type System With Supercritical Initial Data. J Elliptic Parabol Equ 1, 243–262 (2015). https://doi.org/10.1007/BF03377379

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  • DOI: https://doi.org/10.1007/BF03377379

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