Asymptotic profiles of a diffusive mussel–algae system in closed advective environments

Abstract

In this paper, we are concerned with a system modeling the interaction of mussels and algae, where the advection pushes algae in one direction but not out of the domain. We obtain the influence of diffusion and advection on positive steady states. As the advection rate goes to infinity, the individuals concentrate at the downstream end. When the diffusion rate of the algae tends to zero, a part of algae concentrates at the downstream end, the rest part of algae disperses in a non-homogeneous manner; and the density of mussels is positive on the entire habitat. Our results show that the impact of advection on the spatial distribution is virtual.