Special Session 19: Stochastic Partial Differential Equations

Singular limit for a stochastic Allen-Cahn equation with nonlinear diffusion

Danielle Hilhorst
CNRS and University Paris-Sud
France
Co-Author(s):    Perla El Kettani, Yong Jung Kim and Hyunjoon Park
Abstract:
We study a stochastic Allen-Cahn equation with nonlinear diffusion and a mild random noise on a bounded domain in Rn. We consider initial data that satisfy some non-degeneracy conditions, and prove that steep transition layers develop within a very short time. We then study the motion of these transition layers and derive a stochastic motion law for the sharp interface limit.