On the short time asymptotic of the stochastic Allen–Cahn equation
Weber, Hendrik
Ann. Inst. H. Poincaré Probab. Statist., Tome 46 (2010) no. 1, p. 965-975 / Harvested from Project Euclid
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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.
Publié le : 2010-11-15
Classification:  Stochastic reaction–diffusion equation,  Sharp interface limit,  Randomly perturbed boundary motion,  35R60,  53C44 
@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/