Stability of planar waves in a Lotka-Volterra system

This paper is concerned with the large time behavior of disturbed planar fronts in the Lotka-Volterra system in Rn(n⩾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=+∞. And then we prove that the planar front is asymptotically stable in L∞(Rn) under ergodic perturbations, which include quasi-periodic and almost periodic ones as special cases.