Acceleration of Propagation in Nonlocal Dispersal Equations

讲座时间 Datetime: 2022年7月16日，星期六，10:00-11:30

地点 Venue: 腾讯线上会议：971569134

主持人 Host：唐德

报告人 Speaker: 李万同

单位 Affiliation:兰州大学

报告摘要 Abstract:

In this talk, we focus on the acceleration propagation in diffusion phenomena. It is well-known that the solution of a monostable nonlocal dispersal scalar equation spreads at a finite speed when the kernel is thin-tailed and propagates by accelerating when the kernel has a heavy tail (the fat-tailed). However, in such systems, we find that one species can propagate by accelerating although its dispersal kernel is thin-tailed, which is a new and interesting phenomenon. This gives us a new understanding of the cooperation relation in the spatial propagation of nonlocal dispersal cooperative systems. Furthermore, we determine the spreading speed of an epidemic model with nonlocal diffusion and free boundary and show that when spreading is successful, the asymptotic spreading speed is finite or infinite depending on whether a threshold condition is satisfied by the kernel function governing the spatial dispersal of the agents.