Propagation of chaos for the Keller-Segel equation over bounded domains

Abstract

In this paper we rigorously justify the propagation of chaos for the parabolic-elliptic Keller-Segel equation over bounded convex domains. The boundary condition under consideration is the no-flux condition. As intermediate steps, we establish the well-posedness of the associated stochastic equation as well as the well-posedness of the Keller-Segel equation for bounded weak solutions.

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• Well-posedness and approximation of reflected McKean-Vlasov SDEs with applications
• Learning interacting particle systems: diffusion parameter estimation for aggregation equations
• On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
• Quantitative estimate of the overdamped limit for the Vlasov-Fokker-Planck systems
• The microscopic derivation and well-posedness of the stochastic Keller-Segel equation