Propagation Dynamics of a Nonlocal Time-Space Periodic Reaction-Diffusion Model with Delay

主讲人：王智诚  兰州大学教授

时间：2021年10月10日9：00

地点：腾讯会议 478 127 447

举办单位：数理学院

主讲人介绍：王智诚，男，甘肃庄浪人，兰州大学数学与统计学院教授，博士生导师。1994年本科毕业于西北师范大学，2007年在兰州大学获理学博士学位。在Trans.  AMS、Arch. Rational Mech. Anal.、SIAM J. Math. Anal.、SIAM J. Appl.  Math.、JMPA、Calc. Var. PDE、JDE、JDDE、Nonlinearity、J. Math. Biol.、J. Nonlinear  Sci等杂志发表SCI论文90多篇。2011和2019年分别获得甘肃省自然科学二等奖，主持完成两项国家自然科学基金面上项目以及教育部博士点基金等多项省部级项目，正在主持一项甘肃省基础研究创新群体项目、一项国家自然科学基金面上项目并参加一项国家自然科学基金重点项目。目前担任两个SCI杂志International  J. Bifurc. Chaos 和Mathematical Biosciences and Engineering (MBE) 的编委（Associate  editor）。

内容介绍：In this talk, we consider a nonlocal time-space periodic reaction-diffusion  model with stage structure. We first prove the existence and global attractivity  of time-space periodic solution for the model. Next, by a family of principal  eigenvalues associated with linear operators, we characterize the asymptotic  speed of spread of the model in the monotone and non-monotone cases.  Furthermore, we introduce a notion of transition semi-waves for the model, and  then by constructing appropriate upper and lower solutions, and using the  results of the asymptotic speed of spread, we show that transition semi-waves  exist when their wave speeds are above than a critical speed, and transition  semi-waves do not exist anymore when their wave speeds are less than the  critical speed. It turns out that the asymptotic speed of spread coincides with  the critical wave speed of transition semi-waves. Finally, numerical simulations  for various cases are carried out to support our theoretical results.