Title: The role of protection zone on species spreading governed by a reaction–diffusion model with strong Allee effect

Presenter: Peng Rui

Abstract: It is known that a species dies out in the long run for small initial data if its evolution obeys a reaction of bistable nonlinearity. Such a phenomenon, which is termed as the strong Allee effect, is well supported by numerous evidence from ecosystems, mainly due to the environmental pollution as well as unregulated harvesting and hunting. To save an endangered species, we introduce a protection zone that is governed by a Fisher-KPP nonlinearity, and examine the dynamics of a reaction–diffusion model with strong Allee effect and protection zone. We show the existence of two critical values 0 < L_∗ ≤ L^∗, and prove that a vanishing-transition-spreading trichotomy result holds when the length of protection zone is smaller than L_∗; a transition-spreading dichotomy result holds when the length of protection zone is between L_∗ and L^∗; only spreading happens when the length of protection zone is larger than L^∗. This suggests that the protection zone works when its length is larger than the critical value L^∗. Furthermore, we compare two types of protection zone with the same length: a connected one and a separate one, and our results reveal that the former is better for species spreading than the latter.

Presenter Introduction: Peng Rui, Professor of Jiangsu Normal University

Inviter: Hu Xijun, Professor of School of Mathematics

Time: 14:30, May 21 (Tuesday)

Location: Hall 1238, Block B, Zhixin Building, Central Campus

Hosted by: School of Mathematics, Shandong University