Concentration Phenomena of a Semilinear Elliptic Equation with Large Advection in an Ecological Model
arXiv:1003.5632 · doi:10.1016/j.jde.2010.08.028
Abstract
We consider a reaction-diffusion-advection equation arising from a biological model of migrating species. The qualitative properties of the globally attracting solution are studied and in some cases the limiting profile is determined. In particular, a conjecture of Cantrell, Cosner and Lou on concentration phenomena is resolved under mild conditions. Applications to a related parabolic competition system is also discussed.