Asymptotic profiles of positive steady states in a reaction–diffusion benthic–drift model

Abstract

In this paper, we investigate a reaction–diffusion–advection benthic–drift model, where the population is divided into two interacting groups: individuals dispersing in the drift zone and individuals living in the benthic zone. For different growth types of the benthic population, we present asymptotic profiles of positive steady states in three cases: (i) large advection; (ii) small diffusion of the drift population; and (iii) large diffusion of the drift population. We prove that in case (i) both the benthic and drift individuals concentrate only at the downstream end; in case (ii), both benthic and drift population reside inhomogeneously in $(0,L)$, stay away from the upstream end $x=0$, and concentrate only at the downstream $x=L$; and in case (iii), the drift species distributes evenly on the entire habitat and the benthic species distributes inhomogeneously throughout the habitat. The result supplements the dynamical behaviors of benthic–drift models developed in earlier works and is also of its own interest.