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arXiv · 1003.4182

Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension

Vincent Calvez·Lucilla Corrias·Mohammed Abderrahman Ebde
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Abstract

This paper is devoted to the analysis of the classical Keller-Segel system over $\mathbb{R}^d$, $d\geq 3$. 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 when dealing with the parabolic-elliptic case are: local existence without smallness assumption on the initial density, global existence under an improved smallness condition and comparison of blow-up criteria. A new concentration phenomenon criteria for the fully parabolic case is also given. The analysis is completed by a visualization tool based on the reduction of the parabolic-elliptic system to a finite-dimensional dynamical system of gradient flow type, sharing features similar to the infinite-dimensional system.

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Vincent Calvez, Lucilla Corrias, Mohammed Abderrahman Ebde. 2010-03-22. Blow-up, concentration phenomenon and global existence for the Keller-Segel model in high dimension. https://arxiv.org/abs/1003.4182

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