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We introduce recent work studying systems of diffusion that interact through their reflection term (local time). We discuss how the hydrodynamic limit of such systems, i.e. the large-scale behavior of the empirical process, will converge to a nonlinear PDE whose solution exhibits interaction with the past values at the boundary. If time allows, we will discuss aspects of the proofs and how the uniqueness of such PDEs follows from a stochastic representation.
