AI 中文总结
该研究采用哈密顿-雅可比方程的粘性解理论，对移位生境中时滞非局部扩散方程的传播速度分类，揭示了非局部选择机制的方向不对称性和时滞不敏感性，确定了生境锁定消除时滞减速作用的阈值条件。
AI 中文摘要
本文研究移位生境中时滞非局部扩散方程的空间传播动力学。我们利用哈密顿-雅可比方程的粘性解理论，对传播速度进行完整分类。特别地，我们推导了变分公式，明确表征了三类区域（局部决定区、非局部选择区和锁定区）中，传播速度如何依赖初始数据的衰减率、生境移位速度和成熟时滞。我们揭示了非局部选择机制中独特的方向不对称性和一种新的时滞不敏感性现象，还确定了生境锁定效应消除时滞经典减速作用的阈值条件。
英文摘要
This paper is concerned with the spatial propagation dynamics of time-delayed nonlocal diffusion equations in shifting habitats. We employ the theory of viscosity solutions for Hamilton-Jacobi equations to provide a complete classification of the spreading speeds. In particular, we derive variational formulas that explicitly characterize how these speeds depend on the decay rate of the initial data, the habitat shifting speed, and the maturation delay across three regimes: locally determined, nonlocally selected, and locked. We reveal a distinct directional asymmetry in the nonlocal selection mechanism and a novel delay-insensitivity phenomenon. We also establish the threshold conditions under which the habitat locking effect eliminates the classical decelerating role of time delay.
