Asymptotic Behavior of the Principal Eigenvalue for Cooperative Elliptic Systems and Applications
Asymptotic Behavior of the Principal Eigenvalue for Cooperative Elliptic Systems and Applications
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DOI：
10.1007/s10884-015-9504-4
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发表时间：
2016-03
影响因子：
1.3
通讯作者：
King-Yeung Lam;Y. Lou
中科院分区：
文献类型：
--
作者：
King-Yeung Lam;Y. Lou
研究了具有小扩散率的一般线性合作椭圆型方程组的主特征值的渐近性态。作为应用，我们证明了如果一个合作的常微分方程组存在唯一的全局渐近稳定的正平衡点，那么相应的反应扩散方程组在Neumann边界条件或Robin边界条件下也存在唯一的全局渐近稳定的正平衡点，只要扩散系数足够小.当扩散系数趋于零时，反应扩散系统的正定态一致收敛到相应动力学系统的平衡点。
The asymptotic behavior of the principal eigenvalue for general linear cooperative elliptic systems with small diffusion rates is determined. As an application, we show that if a cooperative system of ordinary differential equations has a unique positive equilibrium which is globally asymptotically stable, then the corresponding reaction-diffusion system with either the Neumann boundary condition or the Robin boundary condition also has a unique positive steady state which is globally asymptotically stable, provided that the diffusion coefficients are sufficiently small. Moreover, as the diffusion coefficients approach zero, the positive steady state of the reaction-diffusion system converges uniformly to the equilibrium of the corresponding kinetic system.