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

Hendrik Weber

doi:10.1214/09-AIHP333

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

Hendrik Weber

Department of Mathematical Sciences

Rheinische Friedrich-Wilhelms-Universität Bonn

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16 Citations (SciVal)

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 [Acta Math. Sin (Engl. Ser.) 15 (1999) 407–438] in spatial dimension n=2 to arbitrary dimensions.

Original language	English
Pages (from-to)	965-975
Journal	Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
Volume	46
Issue number	4
DOIs	https://doi.org/10.1214/09-AIHP333
Publication status	Published - 1 Nov 2010

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http://projecteuclid.org/euclid.aihp/1288878332

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

Abstract

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