Generation of fine transition layers and their dynamics for the stochastic Allen--Cahn equation
Matthieu Alfaro, Dimitra C. Antonopoulou, Georgia Karali, Hiroshi Matano · arXiv (Cornell University) · 2018
We study an $\ep$-dependent stochastic Allen--Cahn equation with a mild random noise on a bounded domain in $\mathbb{R}^n$, $n\geq 2$. Here $\ep$ is a small positive parameter that represents formally the thickness of the solution interface, while the mild noise $ξ^\ep(t)$ is a smooth random function of $t$ of order $\mathcal O(\ep^{-γ})$ with $0