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Springer, Journal of Mathematical Biology, 1(63), p. 1-32, 2010

DOI: 10.1007/s00285-010-0357-5

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

Journal article published in 2010 by Piotr Biler, Lucilla Corrias, Jean Dolbeault ORCID
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This paper is available in a repository.

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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.