Consider the Allen-Cahn equation with small diffusion perturbed by a space time white noise of intensity . In the limit, , solutions converge to the noise free problem in the 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 differential equations. Computations are described, which support the asymptotic derivation.
Submitted April 18, 2000. Published June 15, 2000.
Math Subject Classifications: 60H15, 74N20, 45M05.
Key Words: dynamics of phase-boundaries, stochastic partial differential equations, asymptotics.
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