Title: The Principal Eigenvalue for Degenerate Periodic Reaction-Diffusion Systems

Abstract: The theory of the principal eigenvalue is established for the eigenvalue problem associated with a linear time-periodic parabolic cooperative system with some zero diffusion coefficients. The lack of compactness for the solution map of the system is the most difficulty of this project. We use a generalized Krein-Rutman theorem to overcome it. The main contribution of this work is to figure out the essential spectrum of the corresponding system. This talk is based on a joint work with Prof.Xing Liang and Prof. Xiao-Qiang Zhao.