A McKean-Vlasov SDE and particle system with interaction from reflecting boundaries.

We consider a one-dimensional McKean-Vlasov SDE on a domain and the associated mean-field interacting particle system. The peculiarity of this system is the combination of the interaction, which keeps the average position prescribed, and the reflection at the boundaries; these two factors make the effect of reflection non local. We show pathwise well-posedness for the McKean-Vlasov SDE and convergence for the particle system in the limit of large particle number.