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 [Acta Math. Sin (Engl. Ser.) 15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.
|Journal||Annales de l'Institut Henri Poincaré, Probabilités et Statistiques|
|Publication status||Published - 1 Nov 2010|