Blow-up, Concentration Phenomenon and Global Existence for the Keller–Segel Model in High Dimension

By Vincent Calvez, Lucilla Corrias, Mohamed Abderrahman Ebde. 2010

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This article is devoted to the analysis of the classical Keller–Segel system over ℝ d , d ≥ 3. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and in the fully parabolic case. The main results in the parabolic-elliptic case are: local existence without smallness assumption on the initial density and a quantified blow-up rate, global existence under an improved smallness condition and comparison of blow-up criteria. A new concentration phenomenon for the fully parabolic case is also given.

Subfields: Cell Biology, Modeling and Simulation, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/0139783734d0d2ece60e6bc85b18c27363a51567