  In this article, we consider the ABC model in contact with slow/fast
reservoirs. In this model, there is at most one particle per site, which can be
of type $\alpha\in\{A,B,C\}$ and particles exchange positions in the discrete
set of points $\{1,\cdots, N-1\}$ with a weakly asymmetric rate that 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 with a rate that depends
on the type of particles involved. We prove that the hydrodynamic limit, in the
diffusive time scale, is given by a system of non-linear coupled equation with
several boundary conditions, that depend on the strength of the reservoir's
action.
