Hydrodynamics for the ABC model with slow/fast boundary

Abstract

In this article, we consider the ABC model in contact with slow/fast reservoirs. In this model, there is one particle per site, which can be of type α∈{A,B,C} and particles exchange positions in the discrete set of points {1,…,N−1} with a rate which is weakly asymmetric and depends on the type of particles involved in the exchange mechanism. At the boundary points x=1,N−1 particles can be injected or removed, and the rate at which this happens depends on the type of particles involved. We prove the hydrodynamic limit, in the diffusive time scale, given by a system of non-linear coupled equations with several boundary conditions, that depend on the strength of the reservoir’s action.