Long time behavior of a diffusive competition model

Abstract

<p>In this paper we investigate the long time behavior of a diffusive competition model in a bounded domain <i>Ω</i> ⊂ 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→∞ <i>u</i>(<i>x, t</i>) = <i>s</i>, lim_t→∞ υ(<i>x, t</i>) = 1 - <i>s</i> uniformly on <i>Ω</i> (with hat) for some <i>s</i> ∈ [0, 1] provided that either <i>d</i>₁ = <i>d</i>₂, or <i>d</i>₁ and <i>d</i>₂ are suitably large.</p>