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

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 in spatial dimension $n=2$ to arbitrary dimensions.

11 pages

References in corpus (1)

• Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem

Cited by in corpus (5)

• Analysis of Some Splitting Schemes for the Stochastic Allen-Cahn Equation
• Tightness for a stochastic Allen--Cahn equation
• Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
• Weak solutions to the sharp interface limit of stochastic Cahn-Hilliard equations
• A stochastically perturbed mean curvature flow by colored noise