Floquet bundle theory serves as a natural extension of the eigenvalue theory for elliptic and periodic parabolic operators to the spectral theory of non-autonomous, non-periodic parabolic operators, which provides a useful spectral tool for studying threshold dynamics in more general non-autonomous systems. In this work, we first extend several fundamental properties of the principal eigenvalue to the normalized principal Floquet bundle of non-autonomous, non-periodic parabolic operators, and obtain a series of parallel results. Furthermore, we focus on the asymptotic behavior of the principal Floquet exponent with respect to the generalized frequency and diffusion rate for the operator under homogeneous Neumann boundary conditions.  Finally, we employ the normalized principal Floquet bundle to define two critical numbers (as extensions of the basic reproduction number) for a non-autonomous spatially diffusive SIS epidemic model, examine the extinction and weak persistence of the disease, and investigate the limiting behavior of the basic reproduction numbers with respect to the generalized frequency and diffusion rate.

报告人简介

兰州大学教授，博士生导师，萃英学者特聘教授。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。主要研究方向为微分方程与动力系统理论，主要成果发表在Arch. Rational Mech. Anal.、JMPA、Trans. AMS、Indiana Univ. Math. J.、SIAM J. Math. Anal.、SIAM J. Appl. Math.、Israel J. Math.、Sci. China MATH.、CVPDE、JDE、JGA、Nonlinearity、J. Nonlinear Sci.、J. Math. Biol.等杂志上。2010年入选教育部新世纪优秀人才支持计划，2011和2020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，主持多项国家自然科学基金面上项目和一项甘肃省基础研究创新群体项目，参与完成一项国家自然科学基金重点项目。目前担任杂志International  J.  Bifurc. Chaos 和Math. Biosci. Engineering 的编委。