Long time behavior of a diffusive competition model

In this paper we investigate the long time behavior of a diffusive competition model in a bounded domain Ω⊂RnΩ⊂Rn with no-flux boundary condition. This model comes from the study of the effect of migration (dispersal) (Dockery et al., 1998; Lou, 2006). We prove that limt→∞u(x,t)=slimt→∞u(x,t)=s, limt→∞v(x,t)=1−slimt→∞v(x,t)=1−s uniformly on Ω̄ for some s∈[0,1]s∈[0,1] provided that either d1=d2d1=d2, or d1d1 and d2d2 are suitably large.