报告题目：Asymptotic spreading for a diffusive chemostat system

主讲人：林国教授

时 间：2022年9月19日（周一）晚上19：30

地 点：腾讯会议（会议号867-375-069）

主办单位：理学院

主讲人简介：

林国，男，理学博士，兰州大学数学与统计学院教授。主要研究领域为微分方程与动力系统，特别关注一些经典反应扩散模型的传播动力学行为，尤其致力于非合作耦合系统的空间传播理论研究。研究工作获得国家自然科学基金等项目资助，研究成果分别于2011年和2021年获得甘肃省自然科学二等奖。

摘要:

This talk presents the dynamics that one microorganism spatially expands with two nutrients in space-time periodic environment. The generalized principal eigenvalue defined by the linear periodic parabolic operator is applied as a threshold to discuss the associated initial value problem. When the generalized principal eigenvalue is nonnegative, the solutions approach to the microorganism-extinction equilibrium uniformly. When the generalized principal eigenvalue is negative, the spreading speeds of the model are established when the initial distribution of microorganism has nonempty compact support, which are determined by a family of periodic parabolic eigenvalue problems.  In the homogeneous environment, we show that the solutions locally uniformly converge to the microorganism-existent steady state by constructing upper and lower solutions. Finally, numerical simulations are performed to illustrate that the leftward or rightward spreading speed is approximately a constant under various circumstances.