Propagation of chaos for a subcritical Keller–Segel model

Godinho, David; Quiñinao, Cristobal

Annales de l'I.H.P. Probabilités et statistiques, Tome 51 (2015) no. 3, pp. 965-992.

Cet article traite de l’équation de Keller–Segel dans un cadre sous-critique. À l’aide du système de particules en lien avec cette équation, nous montrons des résultats d’existence et d’unicité, puis la propagation du chaos pour ce dernier. Plus précisément, nous montrons que la mesure empirique du système tend vers l’unique solution de l’équation limite lorsque le nombre de particules tend vers l’infini.

This paper deals with a subcritical Keller–Segel equation. Starting from the stochastic particle system associated with it, we show well-posedness results and the propagation of chaos property. More precisely, we show that the empirical measure of the system tends towards the unique solution of the limit equation as the number of particles goes to infinity.

Mots clés : Keller–Segel, propagation of chaos, well-posedness

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