Limiting structure of steady-states to the Lotka–Volterra competition model with large diffusion and advection
Limiting structure of steady-states to the Lotka–Volterra competition model with large diffusion and advection
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DOI：
10.1016/j.jde.2014.11.016
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发表时间：
2015-03
影响因子：
2.4
通讯作者：
Kousuke Kuto;T. Tsujikawa
中科院分区：
文献类型：
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作者：
Kousuke Kuto;T. Tsujikawa
本文研究的是具有扩散和平流的平稳 Lotka-Volterra 竞争模型的诺伊曼问题。首先我们通过Leray-Schauder 度理论得到非常数解存在的一些充分条件。接下来，我们推导出一个极限系统，其中一种物质的扩散和平流趋于无穷大。限制系统可以简化为具有非局部约束的半线性椭圆方程。在简化的一维情况下，极限系统非常数解的全局分岔结构可以根据系数进行分类。例如，该结构涉及连接两个不同的奇异扰动状态（边界层解和内层解）的全局分叉曲线。我们的证明采用了关联积分映射的水平集分析。
This paper is concerned with the Neumann problem of a stationary Lotka–Volterra competition model with diffusion and advection. First we obtain some sufficient conditions of the existence of nonconstant solutions by the Leray–Schauder degree theory. Next we derive alimiting systemas diffusion and advection of one of the species tend to infinity. The limiting system can be reduced to a semilinear elliptic equation with nonlocal constraint. In the simplified 1D case, the global bifurcation structure of nonconstant solutions of the limiting system can be classified depending on the coefficients. For example, this structure involves a global bifurcation curve which connects two different singularly perturbed states (boundary layer solutions and internal layer solutions). Our proof employs a levelset analysis for the associate integral mapping.