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

被引：13
作者：
Weber, Hendrik [1 ]
机构：
[1] Univ Bonn, Inst Appl Math, D-53115 Bonn, Germany
来源：
ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2010年 / 46卷 / 04期
关键词：
Stochastic reaction-diffusion equation; Sharp interface limit; Randomly perturbed boundary motion; MEAN-CURVATURE; LEVEL SETS; MOTION; INTERFACES; LIMIT; FLOW;
D O I：
10.1214/09-AIHP333
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
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.
引用
收藏
页码：965 / 975
页数：11
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