报告题目：

Global Dynamics of a Lotka-Volterra Competition-Diffusion

-Advection System in Heterogeneous Environments

报告时间：2018年5月19日上午9:00-12:00

报告地点：数学与统计学院金融实验室

报告人：加拿大纽芬兰大学  赵晓强教授

报告人简介：

赵晓强, 加拿大纽芬兰大学教授。主要从事应用动力系统和生物数学领域的研究工作。迄今为止，在 “Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 J. Reine Angew. Math.、 J. Math. Pures Appl.、 SIAM J. Math. Anal、 SIAM J. Appl. Math.、 J. Nonlinear Science、J. Funct. Anal.、 J. Differ. Equations、J. Math. Biology、Bull. Math. Biology” 等国际著名期刊上发表学术论文100余篇，并著有 “Dynamical Systems in Population Biology（Springer-Verlag）”。此外，赵教授目前担任加拿大数学会主办杂志 “Canadian Mathematical Bulletin” 的主编和另外两个国际动力系统期刊的编委。

报告摘要：

We study a Lotka-Volterra type reaction-diffusion-advection system, which describes the competition for the same resources between two aquatic species undergoing different dispersal strategies, as reflected by their diffusion and/or advection rates. For the non-advective case, a complete classification of the global dynamics was established by He and Ni already. However, the key ideas developed in the earlier works do not appear to work when advection terms are involved. By assuming the resource function is decreasing in the spatial variable, we prove the non-existence of co-existence steady state and perform sufficient analysis on the local stability of two semi-trivial steady states, where new techniques are introduced to overcome the difficulty caused by the non-analyticity of stationary solutions as well as the diffusion-advection type operators. Combining these two aspects with the theory of abstract competitive systems, we finally obtain the global dynamics, which suggests that the competitive exclusion principle holds in most situations.