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On the short time asymptotic of the stochastic Allen–Cahn equation
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Weber, Hendrik (2010) On the short time asymptotic of the stochastic Allen–Cahn equation. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol.46 (No.4). pp. 965-975. doi:10.1214/09-AIHP333 ISSN 0246-0203.
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Official URL: http://dx.doi.org/10.1214/09-AIHP333
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.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques | ||||
Publisher: | Institute of Mathematical Statistics | ||||
ISSN: | 0246-0203 | ||||
Official Date: | 2010 | ||||
Dates: |
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Volume: | Vol.46 | ||||
Number: | No.4 | ||||
Page Range: | pp. 965-975 | ||||
DOI: | 10.1214/09-AIHP333 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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