Spreading speeds for multidimensional reaction–diffusion systems of the prey–predator type
Spreading speeds for multidimensional reaction–diffusion systems of the prey–predator type
复制标题
DOI：
10.1007/s00526-019-1576-2
复制
发表时间：
2019-07
影响因子：
2.1
通讯作者：
A. Ducrot;T. Giletti;H. Matano
中科院分区：
文献类型：
--
作者：
A. Ducrot;T. Giletti;H. Matano
研究了一类双组分反应扩散系统解的扩展性质，其中包括作为特例的食饵-捕食系统。通过扩展属性，我们指的是从局部化（即紧支持）初始数据开始的解前沿的长时间行为。虽然文献中有关于这种系统存在行波的结果，但对于具有紧支持初始数据的解所表现出的传播现象所知甚少——至少在理论上是如此。主要的困难来自这样一个事实，即比较原则不适用于这样的系统。此外，众所周知的行波技术，如不动点定理和相位肖像分析，并不适用于扩频前。在本文中，我们首先证明了扩散是在确定的扩散速度下发生的。有趣的是，在某些情况下，一个解决方案中可能会出现两个不同速度的独立前沿——一个是猎物的，另一个是捕食者的。
We investigate spreading properties of solutions of a large class of two-component reaction–diffusion systems, including prey–predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts that start from localized (i.e. compactly supported) initial data. Though there are results in the literature on the existence of travelling waves for such systems, very little has been known—at least theoretically—about the spreading phenomena exhibited by solutions with compactly supported initial data. The main difficulty comes from the fact that the comparison principle does not hold for such systems. Furthermore, the techniques that are known for travelling waves such as fixed point theorems and phase portrait analysis do not apply to spreading fronts. In this paper, we first prove that spreading occurs with definite spreading speeds. Intriguingly, two separate fronts of different speeds may appear in one solution—one for the prey and the other for the predator—in some situations.