Stochastic perturbations of the Allen-Cahn equation

Consider the Allen-Cahn equation with small diusion 2 perturbed by a space time white noise of intensity . In the limit, =1=2! 0, solutions converge to the noise free problem in the L2 norm. Under these conditions, asymptotic results for the evolution of phase boundaries in the deterministic setting are extended, to describe the behaviour of the stochastic Allen-Cahn PDE by a system of stochastic dierential equations. Computations are described, which support the asymptotic derivation. Key Words dynamics of phase-boundaries, stochastic partial dierential equations, Asymptotics. AMS Subject Classications 60H15, 74N20, 45M05