发表机构
School of Mathematics and Statistics, Lanzhou University; Department of Mathematics, University of Miami（兰州大学数学与统计学院; 迈阿密大学数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究道路-田野反应扩散捕食者-被捕食者模型的渐近传播速度，通过逐点比较与截断系统约化，刻画了捕食者与被捕食者的入侵速度及其方向依赖性。
AI 中文摘要
本文致力于研究道路-田野反应扩散捕食者-被捕食者系统的渐近传播速度，在该系统中，捕食者在直线 $\R\times \{0\}$ 上的扩散速度快于在半平面 $\R\times (0,+\infty)$ 中的扩散速度。我们通过利用捕食者不存在时被捕食者的入侵速度，以及被捕食者饱和时捕食者的入侵速度，对具有紧支撑初始值的系统解的传播性质给出了精确刻画。值得注意的是，由于直线可能在某个方向锥内加速捕食者的扩张，捕食者的入侵速度随方向而变化。为克服捕食者-被捕食者相互作用与道路-田野相互作用耦合带来的困难，我们首先推导捕食者与被捕食者之间的逐点比较，然后将系统中捕食者的分量约化为一个依赖于被捕食者入侵速度的截断田野-道路系统。通过利用单物种田野-道路模型的已知结果，我们进一步证明了截断系统的传播性质。这一步非常关键。一旦建立了截断系统的传播性质，我们就可以通过应用比较原理和矛盾论证，并构造适当的Lyapunov泛函，获得原始系统解的预期传播性质。
英文摘要
This paper is devoted to studying asymptotic spreading speeds of a road-field reaction-diffusion predator-prey system, in which predators diffuse faster on the straight line $\R\times \{0\}$ than in the half plane $\R\times (0,+\infty)$. We give a sharp characterization of the spreading properties of solutions of the system with compactly supported initial values by appealing to the invasion speed of the prey when predators are absent, and the invasion speed of predators when the prey is saturated. Notably, since the line may accelerate the expansion of predators in a cone of directions, the invasion speed of predators varies with the direction. To overcome the difficulty arising from the coupling between the predator-prey interaction and the road-field interaction, we first derive pointwise comparisons between predators and the prey and then reduce the components of predators in the system to a truncated field-road system depending on the invasion speed of the prey. By using known results for the single-species field-road model, we further show the propagation properties of the truncated system. This step is very crucial. Once the propagation properties of the truncated system are established, we can obtain the expected spreading properties of solutions to the original system by applying the comparison principle and contradiction arguments, and constructing appropriate Lyapunov functionals.
