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

TL;DR

This paper studies a two-species particle system with boundary interactions and bulk dynamics, deriving nonlinear reaction-diffusion equations as the hydrodynamic limit in infinite volume.

Contribution

It introduces a generalized contact process with exchange dynamics and boundary mechanisms, providing a rigorous derivation of hydrodynamic equations for the system.

Findings

Law of large numbers for densities and current established

Limiting behavior described by nonlinear reaction-diffusion equations

Boundary conditions modeled by Dirichlet conditions

Abstract

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.