ERGODICITY FOR THE PHASE-FIELD EQUATIONS PERTURBED BY GAUSSIAN NOISE

Abstract

We prove that the transition semigroup associated with the phase-field equations perturbed by a Gaussian noise has an invariant measure and it is irreducible and strong Feller. This implies by Doob's theorem that it possesses a unique invariant measure which is ergodic and strongly mixing. This implies the ergodicity of the flow associated with the phase-field model of phase transition in the sense of Birkhoff–von Neumann theorem. Such a result seems to be new in this context.