生境变化与竞争系统中的入侵前沿：哈密尔顿-雅可比方法与非局部效应
Invasion Fronts in Shifting Habitats and Competition Systems: A Hamilton-Jacobi Approach and Nonlocal Effects
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中文总结 AI 辅助
该研究综述了反应-扩散方程传播现象的进展，介绍哈密尔顿-雅可比方法，探讨非局部拉拽型前沿等内容，还证明了移动环境中入侵波对数修正的新结果。
中文摘要 AI 辅助
本文综述了生态入侵模型中反应-扩散方程传播现象研究的最新进展。受Shigesada和Kawasaki关于阶段性入侵猜想的启发，我们探讨竞争系统如何产生具有变化生境的有效标量模型。我们介绍用于确定传播速度的哈密尔顿-雅可比方法，并从该视角重新审视Li-Bewick-Shang-Fagan（2014）的结果。随后，我们描述当变化生境连接具有不同正增长率的区域时，非局部拉拽型前沿的出现。我们综述了包括Lam-Yu（2022）和Lam-Nadin-Yu（2025）在内的最新成果。此外，我们还讨论竞争系统、捕食-被捕食系统中的传播现象，以及各类整体解的存在性。最后，我们探讨移动环境中入侵波的对数修正，并证明了一项新结果。
英文摘要
We review recent developments in the study of spreading phenomena in reaction--diffusion equations arising from ecological invasion models. Motivated by the conjecture of Shigesada and Kawasaki on staged invasions, we discuss how competition systems can lead to effective scalar models with shifting habitats. We present the Hamilton--Jacobi approach for determining spreading speeds and revisit the result of {Li--Bewick--Shang--Fagan} (2014) from this perspective. We then describe the emergence of nonlocally pulled fronts when the shifting habitat connects regions of distinct positive growth rates. Recent results including the works of Lam--Yu (2022) and Lam--Nadin--Yu (2025) are surveyed. We also discuss spreading phenomena in competition systems, predator-prey systems, and the existence of various classes of entire solutions. Finally, we discuss the logarithmic correction for invasion waves in moving environments and prove a new result.
