Mean-field limit of a particle approximation for the parabolic-parabolic Keller-Segel model

2022/09/05 by Chen, Li, Wang, Shu, Yang, Rong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.01722

Abstract

In this paper, we study propagation of chaos for the parabolic-parabolic Keller-Segel model with a logarithmic cut-off by establishing a rigorous convergence analysis from a stochastic particle system to the parabolic-parabolic Keller-Segel (KS) equation for any dimension case. Under the assumption that the initial data are independent and identically distributed (i.i.d.) with a common probability density function ρ₀, we rigorously prove the propagation of chaos for this interacting system with a cut-off parameter ε∼ (ln N)^-(2)/(d+2): when N→ ∞, the joint distribution of the particle system is f-chaotic and the measure f possesses a density which is a weak solution to the mean-field parabolic-parabolic KS equation.

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