Selection Mechanism of the Minimal Wave Speed to Competition Models
数学公众报告(120周年校庆系列第30场)
报告题目(Title)：Selection Mechanism of the Minimal Wave Speed to Competition Models
报告人(Speaker)：王飏 博士（山西大学）
地点(Place)：腾讯会议ID：736-726-687
时间(Time)：2022年7月8号下午3:00-4:00
邀请人(Inviter)：黎雄
报告摘要
In this talk, we first introduce Murray's conjecture and Hosono's conjecture related to the selection mechanism of the minimal wave speed of Lotka-Volterra reaction-diffusion competition systems with two-species in the unbalanced competition case and the recent progress on this topic. Then, for Lotka-Volterra reaction-diffusion competition systems with two-species in the weak competition, by the super-subsolutions method, we give some new sufficient conditions on the linear speed selection of the minimal wave speed, which improve previous results, and establish the sufficient conditions on the nonlinear speed selection of such speed. In the end, we show some latest sufficient conditions on the linear speed selection or the nonlinear speed selection of the minimal wave speed of three species reaction-diffusion competition systems via the novel ways of constructing the super-subsolutions. Further, we apply the same ways to obtain the new sufficient conditions on the nonlinear selection mechanism for the minimal wave speed of Lotka-Volterra reaction-diffusion competition systems with two-species in the unbalanced competition case, which increase the ranges of parameters that the minimal wave speed is nonlinearly determined, and promote further the study of Hosono's conjecture.
