Abstract
In this paper, we study the asymptotic profile of the steady state of a reaction-diffusion-advection model in ecology proposed in [E. Pachepsky et al., Theoret. Popul. Biol., 67 (2005), pp. 61--73; D. Speirs and W. Gurney, Ecology, 82 (2001), pp. 1219--1237]. The model describes the population dynamics of a single species experiencing a unidirectional flow. We show the existence of one or more internal transition layers and determine their locations. Such locations can be understood as the upstream invasion limits of the species. It turns out that these invasion limits are connected to the upstream spreading speed of the species and are sometimes subject to the effect of migration from upstream source patches.
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