  We consider a two species process which evolves in a finite or infinite
domain in contact with particles reservoirs at different densities, according
to the superposition of a generalised contact process and a rapid-stirring
dynamics in the bulk of the domain, and a creation/annihilation mechanism at
its boundaries. For this process, we study the law of large numbers for
densities and current. The limiting equations are given by a system of
non-linear reaction-diffusion equations with Dirichlet boundary conditions.
