Title:Principal eigenvalue of elliptic operator with large advection and its applications

Speaker: Professor Lou Yun

Department of Mathematics

Ohio State University

Columbus, USA

Time: June 15, 16:00-17:00

Location: Zhi Yuanlou Room 106.

Abstract: We study the asymptotic behavior, as the coefficient of the advection term

approaches infinity, of the principal eigenvalue of an elliptic operator. As an application,

a Lotka-Volterra reaction-diffusion-advection model for two competing species in a heterogeneous environment is investigated.

The two species are assumed to be identical except their dispersal strategies: one disperses

by random diffusion only, and the other by both random diffusion and advection along

environmental gradient. When the advection is strong relative to random dispersal, both

species can coexist. In some situations, it is further shown that the density of the species

with large advection in the direction of resources is concentrated at the spatial location with

maximum resources. This is based on joint work with Xinfu Chen.