EXPONENTIAL ESTIMATE FOR REACTION-DIFFUSION MODELS

We consider the superposition of a speeded up symmetric simple exclusi on process with a Glauber dynamics, which leads to a reaction diffusio n equation. Using a method introduced in [Y] based on the study of the time evolution of the H--1 norm, we prove that the mean density of pa rticles on microscopic boxes of size N-alpha, for any 12/13 < alpha < 1, converges to the solution of the hydrodynamic equation for times up to exponential order in N, provided the initial state is in the basin of attraction of some stable equilibrium of the reaction-diffusion eq uation. From this result we obtain a lower bound for the escape time o f a domain in the basin of attraction of the stable equilibrium point.