题目🤽🏿‍♀️：The Trichotomy of Solutions and the Description of Threshold Solutions for Periodic Parabolic Equations in Cylinders

报告人📘：王智诚 教授 （兰州大学）

地点🫁：腾讯会议室

时间🍝：2021年11月12日（星期五） 14:00-15:00

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 $|x|\to\infty$.

腾讯会议ℹ️：

https://meeting.tencent.com/dm/KsgKBXftnxL0

会议 ID🤽🏽‍♂️：271 958 341

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