Consider the Allen-Cahn equation with small diffusion f2 perturbed by a space time white noise of intensity a. In the limit, cr/e2 -}0, solutions converge to the noise free problem in the L? 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.
|Number of pages||19|
|Journal||Electronic Journal of Differential Equations|
|Publication status||Published - 1 Dec 2000|
- Dynamics of phase-boundaries
- Stochastic partial differential equations
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