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arXiv · 0908.0580

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

Hendrik Weber
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Abstract

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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Hendrik Weber. 2009-08-05. On the short time asymptotic of the stochastic Allen-Cahn equation. https://doi.org/10.1214/09-aihp333

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