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 nonlocal. We show pathwise well-posedness for the McKean??? Vlasov SDE and convergence for the particle system in the limit of large particle number.