论文标题
在Fisher-KPP方程激发的移动边界问题中，几何形状对生存和灭绝的影响
The Effect of Geometry on Survival and Extinction in a Moving-Boundary Problem Motivated by the Fisher-KPP Equation
论文作者
论文摘要
Fisher-Stefan模型涉及在一个域上求解Fisher-kpp方程，该域的边界根据Stefan样条件而演变。当应用于生物学入侵时，Fisher-Stefan模型减轻了标准Fisher-KPP模型的两个实际局限性。首先，与Fisher-KPP方程不同，Fisher-Stefan模型的解决方案具有紧凑的支持，使人们能够明确定义占领区域和无置区域之间的接口。其次，Fisher-Stefan模型承认了人口灭绝的解决方案，这在Fisher-KPP方程中是不可能的。先前的研究表明，Fisher-Stefan模型中的种群存活或灭绝取决于一维笛卡尔或径向对称几何形状的临界长度。但是，一般二维区域的生存和灭绝行为仍未得到探索。我们结合了Fisher-STEFAN模型的分析和级别的数值模拟，以研究矩形初始条件的生存延伸条件。我们表明，在二维中将关键长度条件推广到关键区域是不足的。取而代之的是，需要了解区域几何形状以确定人口是否会生存还是灭绝。
The Fisher-Stefan model involves solving the Fisher-KPP equation on a domain whose boundary evolves according to a Stefan-like condition. The Fisher-Stefan model alleviates two practical limitations of the standard Fisher-KPP model when applied to biological invasion. First, unlike the Fisher-KPP equation, solutions to the Fisher-Stefan model have compact support, enabling one to define the interface between occupied and unoccupied regions unambiguously. Second, the Fisher-Stefan model admits solutions for which the population becomes extinct, which is not possible in the Fisher-KPP equation. Previous research showed that population survival or extinction in the Fisher-Stefan model depends on a critical length in one-dimensional Cartesian or radially-symmetric geometry. However, the survival and extinction behaviour for general two-dimensional regions remains unexplored. We combine analysis and level-set numerical simulations of the Fisher-Stefan model to investigate the survival-extinction conditions for rectangular-shaped initial conditions. We show that it is insufficient to generalise the critical length conditions to critical area in two-dimensions. Instead, knowledge of the region geometry is required to determine whether a population will survive or become extinct.
