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.
@article{1288878332,
author = {Weber, Hendrik},
title = {On the short time asymptotic of the stochastic Allen--Cahn equation},
journal = {Ann. Inst. H. Poincar\'e Probab. Statist.},
volume = {46},
number = {1},
year = {2010},
pages = { 965-975},
language = {en},
url = {http://dml.mathdoc.fr/item/1288878332}
}
Weber, Hendrik. On the short time asymptotic of the stochastic Allen–Cahn equation. Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, pp. 965-975. http://gdmltest.u-ga.fr/item/1288878332/