  A new non-conservative stochastic reaction-diffusion system in which two
families of random walks in two adjacent domains interact near the interface is
introduced and studied in this paper. Such a system can be used to model the
transport of positive and negative charges in a solar cell or the population
dynamics of two segregated species under competition. We show that in the
macroscopic limit, the particle densities converge to the solution of a coupled
nonlinear heat equations. For this, we first prove that propagation of chaos
holds by establishing the uniqueness of a new BBGKY hierarchy. A local central
limit theorem for reflected diffusions in bounded Lipschitz domains is also
established as a crucial tool.
