学术报告报告题目：Principal Spectral Theory of Nonlocal Dispersal Operators with Almost Periodic Dependence and Its Applications
报 告人：Wenxian Shen教授(Auburn University,USA)
报告时间：2022年6月15日(星期三) 上午9:00-11:00
报告地点：腾讯会议，会议ID：561818896
邀 请人：杨启贵 教授
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数学学院
2022年6月10日
报告摘要：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 there 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 for 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 variouscharacterizations 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.
报告人简介：1987年于北京大学数学系获得硕士学位，1992年于美国乔治亚理工学院数学学院获得博士学位。自1992年于美国奥本大学数学系任教，2002年后成为全职教授。沈文仙教授为国际知名微分方程动力系统专家，多年来致力于研究微分方程中的动力学问题，包括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，拟周期反应扩散方程的渐近动力学行为，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。沈文仙教授现为J. Differential- Equations、 Proc. Amer. Math. Soc.等杂志编委。在Transactions of the American Mathematical Society、SIAM 系列、Journal of Differential Equations、Journal of Dynamics and Differential Equations等国际著名期刊上发表学术论文135余篇，论文被引用超过2663次，主持过多项国家自然科学基金。