学术报告（彭锐 11.24）

摘要：In this talk, I will report our recent work on the principal eigenvalue problem of a time-periodic parabolic operator on a finite network. The network under consideration can support various types of flows, such as water, wind, or traffic. Our focus is on an ecosystem that is subject to natural boundary conditions. We determine the asymptotic behavior of the principal eigenvalue as the diffusion rate approaches zero, or the advection rate approaches infinity. We then apply our results to a single-species population model and two SIS epidemic systems on networks and reveal the substantial impact of the diffusion and advection rates as well as the boundary conditions on the long-time dynamics of the population and the transmission of infectious diseases.