Abstract

In this talk, we will discuss recent progress on the asymptotic behaviour of the principal eigenvalue of some second order operators. Through analyzing the closed orbits of the advection vector field, we obtain a complete result on how the principal eigenvalue converges for large advection.  We also find an unified viewpoint to understand some previous results on this topic, like [Berestycki-Hamel-Nadirashvilli, CMP 2005] and [Chen-Lou, IUMJ2008]. This is a joint work with Shuang Liu and Yuan Lou.