Spatial Patterns when Phases Separate in an Interacting Particle System

Abstract

We consider a one-dimensional Glauber-Kawasaki process which gives rise in the hydrodynamical limit to a reaction diffusion equation with a double-well potential. We study the case when the process starts off from a product measure with zero averages, which, hydrodynamically, corresponds to a stationary unstable state. We prove that at times longer than the hydrodynamical ones the reaction diffusion equation no longer describes the behavior of the system, which in fact leaves the unstable equilibrium. The spatial patterns of the typical configurations when this happens are investigated.