System of interacting particles and nonlinear diffusion reflecting in a domain with sticky boundary

Abstract

We study a system of particles and the nonlinear McKean-Vlasov diffusion that is its limit for weak interactions in Statistical Mechanics, reflecting in a domain with sticky boundary. The interaction takes place in particular in the sojourn condition. We show existence and uniqueness for the nonlinear martingale problem, by a contraction argument on time-change. Then we construct the system of particles by a limiting procedure, and show propagation of chaos towards the nonlinear diffusion.