论文标题
在空间周期性的栖息地中为野外道路模型的传播速度和脉动前线
Spreading speeds and pulsating fronts for a field-road model in a spatially periodic habitat
论文作者
论文摘要
Berestycki，Roquejoffre和Rossi [9]引入了一种称为野外道路模型的反应扩散模型，以在一条线上快速扩散描述生物学入侵。在本文中，我们在异质景观中调查了该模型，并确定了渐近扩散速度C *的存在，并与沿路脉动前线的最小波速相吻合。我们从截断的问题开始，并具有施加的Dirichlet边界条件。我们证明了扩散速度C * r的存在，这与道路方向截断的问题的脉动前线的最小速度相吻合。该参数将动态系统方法与PDE的方法相结合。最后，我们通过广义主特征值方法和渐近方法回到半平面中的原始问题。
A reaction-diffusion model which is called the field-road model was introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological invasion with fast diffusion on a line. In this paper, we investigate this model in a heterogeneous landscape and establish the existence of the asymptotic spreading speed c * as well as its coincidence with the minimal wave speed of pulsating fronts along the road. We start with a truncated problem with an imposed Dirichlet boundary condition. We prove the existence of spreading speed c * R which coincides with the minimal speed of pulsating fronts for the truncated problem in the direction of the road. The arguments combine the dynamical system method with PDE's approach. Finally, we turn back to the original problem in the half-plane via generalized principal eigenvalue approach as well as an asymptotic method.
