论文标题
定期介质中具有快速扩散线的Fisher-KPP模型
A Fisher-KPP model with a fast diffusion line in periodic media
论文作者
论文摘要
我们在呈现快速扩散线的周期性环境中处理人口动态模型。该现象是通过“路场”系统建模的，该系统是在不同维度域中设置的耦合反应扩散方程的系统。在这里，我们首次考虑了反应术语的情况，具体取决于周期性的空间变量，这对其数学困难和应用都引起了极大的兴趣。我们根据适当的广义主特征值的迹象得出了物种生存的必要条件。此外，我们比较了在没有快速扩散线的同一环境中人口的长时间行为，发现该元素对生存机会没有影响。
We treat a model of population dynamics in a periodic environment presenting a fast diffusion line. This phenomenon is modelled via a "road-field" system, which is a system of coupled reaction-diffusion equations set in domains of different dimensions. Here, we consider for the first time the case of a reaction term depending on a spatial variable in a periodic fashion, which is of great interest for both its mathematical difficulties and for its applications. We derive necessary and sufficient conditions for the survival of the species in terms of the sign of a suitable generalised principal eigenvalue. Moreover, we compare the long time behaviour of a population in the same environment without the fast diffusion line, finding that this element has no impact on the survival chances.
