报告人：王智诚教授

报告题目：The trichotomy of solutions and the description of threshold solutions for periodic parabolic equations in cylinders

摘要：In this talk we consider the nonnegative bounded solutions for reaction-advection-diffusion equations of the form $u_{t}-\Delta u+\alpha(t,y)u_{x}=f(t,y,u)$ in cylinders, where $f$ is a bistable or multistable nonlinearity which is $T$-periodic in $t$. We prove that under certain conditions, there are at most three types of solutions for any one-parameter family of initial data: that spread to $1$ for large parameters, vanish to $0$ for small parameters, and exhibit exceptional behaviors for intermediate parameters. We usually refer to the last as the  threshold solutions. It is worth noting that we also give a sufficient condition for solutions to  spread to $1$  by proving a kind of stability of  a pair of diverging traveling fronts.  Furthermore, under the additional conditions, by using super- and sub-solutions, Harnack's inequality and the method of moving hyperplane, we show that any point in the $\omega$-limit set of the threshold solutions is symmetric with respect to $x$,  and exponentially decays to $0$ as $|x|\to\infty$.

报告时间：2021年11月14日14:30-15:30

报告地点：腾讯会议   会议号：190 929 960

报告人简介：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。发表SCI论文90多篇，2010年入选教育部新世纪优秀人才支持计划，2011和2019年分别获得甘肃省自然科学二等奖，2016年入选甘肃省飞天学者特聘教授，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）。