广州数学大讲坛第五期
第四十四讲——兰州大学王新剑博士学术报告
题目：Spreading Speeds and Traveling Wave Solutions of Diffusive Vector-Borne Disease Models without Monotonicity
时间：2022年8月26日（周五）上午9：00-12：00
地点：腾讯会议(会议ID：342 360 785)
报告人：王新剑博士
摘要: In this talk, I will introduce our recent work on the propagation dynamics of diffusive vector-borne disease models in the whole space, which characterize the spatial expansion of the infected hosts and infected vectors. We mainly estimate the spreading speed of the initial value problem and establish the existence, nonexistence, uniqueness, and monotonicity of traveling wave solutions. Due to the lack of monotonicity, the comparison principle cannot be applied directly to this system. The spreading speed is mainly estimated by the uniform persistence argument and generalized principal eigenvalue. We also show that solutions converge locally uniformly to the positive equilibrium. Moreover, it is proven that the spreading speed is the minimal wave speed of traveling wave solutions. Finally, numerical simulations are presented to illustrate the analytical results. This talk is joint work with Prof. Lin Guo, and Prof. Ruan Shigui.
报告人简介：
王新剑,兰州大学数学与统计学院博士研究生,师从林国教授，研究方向为微分方程与动力系统。主要研究兴趣为生物种群模型和流行病模型中的空间传播动力学研究,目前主要关注多种群非单调系统的行波解和初值问题的渐近传播速度。目前在Proc. Roy. Soc. Edinburgh Sect. A，Studies in Applied Mathematics，Applicable Analysis，Commun. Pure Appl. Anal.，Int. J. Biomath.等杂志上发表论文5篇。
