Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model
Analysis of PDEs
2010-10-29 v1
Abstract
The Keller-Segel system describes the collective motion of cells that are attracted by a chemical substance and are able to emit it. In its simplest form, it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration. This paper deals with the rate of convergence towards a unique stationary state in self-similar variables, which describes the intermediate asymptotics of the solutions in the original variables. Although it is known that solutions globally exist for any mass less , a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar variables.
Keywords
Cite
@article{arxiv.0812.4876,
title = {Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model},
author = {Adrien Blanchet and Jean Dolbeault and Miguel Escobedo and Javier Fernández},
journal= {arXiv preprint arXiv:0812.4876},
year = {2010}
}