报告题目：On the Lotka-Volterra competition-diffusion-advection system with dynamical resources

报 告 人：王治安 教授 香港理工大学应用数学系

照    片：

邀 请 人：李善兵

报告时间：2020年11月23日（周一） 10：30-11：30

报告地点：腾讯会议 ID：154 861 037

报告人简介：王治安，香港理工大学应用数学系教授，华中师大本科硕士， 加拿大艾伯塔大学应用数学博士，美国明尼苏达大学应用数学所博士后。从事与生物数学相关的偏微分方程研究，主要研究方向是趋化及其相关模型的建模及理论分析与数值模拟。现担任杂志 DCDS-B编委和香港数学会秘书长, 曾获香港数学会颁发的青年学者奖以及 JMAA杂志最佳论文奖。

报告摘要：We consider a Lotka-Volterra competition-diffusion-advection system with dynamical resources. We show that the system has a unique global classical solution when initial datum is in some appropriate functional space. By constructing appropriate Lyapunov functionals and using LaSalle's invariant principle, we prove that the solution converges to the co-existence steady state exponentially or competitive exclusion steady state algebraically as time tends to infinity in different parameter regimes. Our results reveal that once the resource species has temporal dynamics, the striking phenomenon "slower diffuser always prevails" for given spatially heterogeneous resource no longer exist and two competitors can coexist regardless of their diffusion rates and initial values. When the prey resource is spatially heterogeneous, we use numerical simulations to demonstrate that the phenomenon "slower diffuser always prevails" breaks down if the non-random dispersion strategy amongst competing species is employed.