Long time behavior of a diffusive competition model

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• 作者：Wenjie Ni ; ^{nwj1033159832@163.com" class="auth_mail" title="E-mail the corresponding author} ; Mingxin Wang
• 关键词：Diffusive competition model ; Long time behavior ; Positive equilibrium solutions
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：58
• 期：Complete
• 页码：145-151
• 全文大小：530 K

文摘

In this paper we investigate the long time behavior of a diffusive competition model in a bounded domain Ω⊂Rⁿ$\Omega \subset {\mathbb{R}}^n$ 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${lim}_{t\to \infty }u(x,t)=s$, lim_t→∞v(x,t)=1−s${lim}_{t\to \infty }v(x,t)=1-s$ uniformly on $\bar{\Omega }$ for some s∈[0,1]$s\in [0,1]$ provided that either d₁=d₂$d_1=d_2$, or d₁$d_1$ and d₂$d_2$ are suitably large.