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Article Dans Une Revue Journal of Mathematical Analysis and Applications Année : 2008

Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model

Résumé

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 $8\pi\,$, a smaller mass condition is needed in our approach for proving an exponential rate of convergence in self-similar~variables.
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Dates et versions

hal-00349216 , version 1 (24-12-2008)

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Adrien Blanchet, Jean Dolbeault, Miguel Escobedo, Javier Fernández. Asymptotic behaviour for small mass in the two-dimensional parabolic-elliptic Keller-Segel model. Journal of Mathematical Analysis and Applications, 2008, 361 (2), pp.533-542. ⟨10.1016/j.jmaa.2009.07.034⟩. ⟨hal-00349216⟩
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