走向现代数学学术报告 – 许钊泉教授（No. 986)

报告题目：Forced traveling waves in a population model with mobile and stationary states under a changing environment

报 告 人：许钊泉 教授（暨南大学）

邀 请 人：李健 教授

报告时间：2026年10月28日15点

报告地点：东海岸校区D324

报告摘要：In this talk, I will introduce a population model with mobile and stationary states under a changing environment, which is modeled by a partially degenerate reaction-diffusion equation with a moving variable x+ct. We focus on whether the species could keep up with the changing environment, that is, whether the equation model has a forced traveling wave with speed c, and how the switching rates between mobile and stationary states affect the propagation dynamics. It is shown that there exists a threshold value c*>0, such that the equation model admits a forced traveling wave with speed c if and only if the environment shifting speed c>-c*. Thereby, the species cannot follow the changing environment with speed c if c≤-c*. Compared to the well-known results on the classic Fisher's equation which assumes the population has only mobile state, our result highlights a significant observation: the presence of stationary state in population will reduce the invasion threshold value c*. Moreover, it is proved that such a forced traveling wave is unique and globally stable if c>-c*. This implies that the species can successfully invade new environment as a forced wave if the environment shifting speed c satisfies c>-c*. Some numerical simulations are also provided to illustrate the theoretical results and explain the invasion phenomena of species under environmental changes.

报告人简介：许钊泉，上海交通大学理学博士毕业，现为暨南大学教授，博士生导师。主要从事微分方程动力系统理论及其应用方面研究。相关结果发表在 JDE, JDDE，Nonlinearity, DIE, PAMS, PRSE-A, DCDS-A, JMP, EJAMS, Physica. D 等期刊，获批主持省部级以上项目7项。