Long time behavior of a diffusive competition model

Abstract

In this paper we investigate the long time behavior of a diffusive competition model in a bounded domain Ω ⊂ R n 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 lim t → ∞ u ( x , t ) = s , lim t → ∞ v ( x , t ) = 1 − s uniformly on Ω ̄ for some s ∈ [ 0 , 1 ] provided that either d 1 = d 2 , or d 1 and d 2 are suitably large.