A boundary driven generalized contact process with exchange of particles: Hydrodynamics in infinite volume

We consider a two species process which evolves in a finite or infinite domain in contact with particle reservoirs at different densities, according to the superposition of a generalized 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.