Stochastic Phase Field Equations: Existence and Uniqueness

Abstract.

We consider a conservative system of stochastic PDE's, namely a one dimensional phase field model perturbed by an additive space-time white noise. We prove a global existence and uniqueness result in a space of continuous functions on $\mathbb{R}_{+} \times \mathbb{R}$. This result is obtained by extending previous results of Doering [3] on the stochastic Allen-Cahn equation.