On the short time asymptotic of the stochastic Allen-Cahn equation

Details On the short time asymptotic of the stochastic Allen-Cahn equation On the short time asymptotic of the stochastic Allen-Cahn equation

2009-08-05

arxiv.org/abs/0908.0580v1

Mathematics

Probability

11 pages

Scientific paper

A description of the short time behavior of solutions of the Allen-Cahn
equation with a smoothened additive noise is presented. The key result is that
in the sharp interface limit solutions move according to motion by mean
curvature with an additional stochastic forcing. This extends a similar result
of Funaki in spatial dimension $n=2$ to arbitrary dimensions.

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