The mean-field limit for particle systems with uniform full-rank constraints

Abstract

We consider a particle system with uniform coupling between a macroscopic component and individual particles. The constraint for each particle is of full rank, which implies that each movement of the macroscopic component leads to a movement of all particles and vice versa. Skeletal muscle tissues share a similar property which motivates this work.We prove convergence of the mean-field limit, well-posedness and a stability estimate for the mean-field PDE. This work generalises our previous results from [25] to the case of nonlinear constraints.