SPD

Abstract

We study the stochastic Cahn-Hilliard equation with an additive space-time white noise. We consider the physical potential with a double logarithmic singularity in -1 and +1 in a one-dimensionnal domain. Since the singularities are not strong enough to prevent the solution from going out the physical domain [-1,1], we add two reflection measures in the boundary. We show that the system has a unique invariant measure in order to obtain existence and uniqueness of stationary solution. We also prove some results about ergodicity, exponential mixing and integration by parts formula. This is a joint work with Arnaud Debussche (ENS Cachan Bretagne).