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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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