Planar Waves of the Buffered Bistable System

Abstract

This paper is concerned with the large time behavior of disturbed planar fronts in the buffered bistable system in ${ℝ}^n$ ($n\ge 2$). We first show that the large time behavior of the disturbed fronts can be approximated by that of the mean curvature flow with a drift term for all large time up to $t=+\infty$. And then we prove that the planar front is asymptotically stable in $L^{\infty }({ℝ}^n)$ under ergodic perturbations, which include quasiperiodic and almost periodic ones as special cases.