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Journal Articles Journal of Mathematical Biology Year : 2011

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

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 8π. 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 8π 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 8π, which is forbidden in the parabolic-elliptic case.
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Dates and versions

hal-00411913 , version 1 (31-08-2009)

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Piotr Biler, Lucilla Corrias, Jean Dolbeault. Large mass self-similar solutions of the parabolic-parabolic Keller--Segel model of chemotaxis. Journal of Mathematical Biology, 2011, 63, pp.1-32. ⟨10.1007/s00285-010-0357-5⟩. ⟨hal-00411913⟩
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