报告题目：Principal spectral theory of nonlocal dispersal operators with almost periodic dependence and its applications

主讲人：沈文仙 教授 （美国奥本大学）

时 间：2022年1月8日（周六）上午9：00

地 点：腾讯会议（会议号 146 919 475）

主办单位：理学院

主讲人简介：

沈文仙，美国奥本大学教授，国际知名微分方程动力系统专家。现为国际权威数学杂志 Proc.Amer.Math.Soc.等杂志编委。沈教授多年来致力于研究异质和随机介质理论中的行波解，单调动力系统中的Lyapunov指数理论，非局部扩散算子的谱理论及应用，非自治与随机动力系统以及格动力系统，并获得了许多重要与深刻的结论。特别是与其合作者所发展的非自治单调斜积半流理论已成为处理许多非自治方程动力系统的重要工具。

摘要:

Nonlocal and random dispersal evolution equations are widely used to model diffusive systems in applied sciences. These two types of equations share many properties, but here are also some essential differences between them. In comparison to random dispersal evolution equations, many fundamental dynamical issues for nonlocal dispersal evolution equations are less well understood. This talk is concerned with principal spectral theory or linear nonlocal dispersal evolution equations with almost periodic dependence. We investigate the principal spectral theory of such operators from two aspects: top Lyapunov exponents and generalized principal eigenvalues. Among others, we provide various characterizations of the top Lyapunov exponents and generalized principal eigenvalues, establish the relations between them, and study the effect of time and space variations on them. We also discuss the application of the principal spectral theory to the asymptotic dynamics of nonlinear nonlocal dispersal equations with almost periodic dependence.