Asymptotic analysis of the principal eigenvalue for a spatially discrete and time-periodic problem

时   间：  2023-03-07 08:00 — 10:00

The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some time-periodic and spatially discrete eigenvalue problem. Various asymptotic behaviors of the principal eigenvalue and its monotonocity, as a function of the diffusion rate and frequency, are derived. This leads to the classification of the topological structures of the level sets for the principal eigenvalue, in the plane of frequency and diffusion rate. Our results support the majority of the conjectures proposed for second order time-periodic parabolic operators. A bit surprisingly, when both diffusion rate and frequency are sufficiently large, our analysis suggests a counterexample for one of the conjectures proposed for parabolic operators.