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We consider a two species process which evolves in a finite or infinitedomain in contact with particles reservoirs at different densities, accordingto the superposition of a generalised contact process and a rapid-stirringdynamics in the bulk of the domain, and a creation/annihilation mechanism atits boundaries. For this process, we study the law of large numbers fordensities and current. The limiting equations are given by a system ofnon-linear reaction-diffusion equations with Dirichlet boundary conditions.

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