The nonlocal selection of spreading speed in shifting environments

讲座时间 Datetime: 2022年6月16日，星期四， 15:30-17:00

地点 Venue: 腾讯线上会议：523323720

 主持人 Host：唐德

报告人 Speaker:林经洋

单位 Affiliation:美国俄亥俄州立大学

报告摘要 Abstract:

Since the work of [Potapov and Lewis, 2004] and [Berestycki et al., 2009], there has been a lot of interest in the population dynamics driven by climate change, particularly the persistence and invasion of species as their suitable habitat are shifting poleward. In this project, we study the asymptotic spreading of Kolmogorov-Petrovsky-Piskunov (KPP) fronts in heterogeneous shifting habitats, with any number of shifting speeds, by further developing the method based on Hamilton-Jacobi equations due to Freidlin, Evans and Souganidis. Our framework addresses both reaction-diffusion equations and integro-differential equations with a distributed time-delay. We derive the Hamilton-Jacobi equations (HJE) corresponding to such integro-differential problems, and prove comparison principles under suitable (local) monotonicity assumptions. A challenging aspect is the fact that the Hamiltonians have jump discontinuities. As applications, we observe that for the classical Fisher-KPP equation with shifting heterogeneity, the spreading speed is no longer determined by the formula 2 sqrt (rd), i.e. it may sometimes exceed the level predicted by local conditions. An explanation of the nonlocal mechanism behind the speed enhancement will be given. Some related works, motivated by the conjecture of Shigesada et al. concerning the co-invasion of several competing tree species into an open space, will also be mentioned. This is joint work with Xiao Yu (South China Normal University).