On the short time asymptotic of the stochastic Allen-Cahn equation
نویسنده
چکیده
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 [9] in spatial dimension n = 2 to arbitrary dimensions. Resumé On étudie le comportement de la solution de l’équation de Allen-Cahn perturbée par un bruit stochastique additif et regularisé. Il est demontré que, dans la limite d’un interface singulier, les solutions évoluent selon la courbure moyenne avec un renforcement stochastique additionel. Ceci généralise un résultat de Funaki [9] pour la dimension spatial d = 2 à une dimension quelquonque.
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