Dynamics of Lotka-Volterra diffusion-advection competition system with heterogeneity vs homogeneity

This paper mainly studies the dynamics of a Lotka-Volterra reaction-diffusion-advection model for two competing species which disperse by both random diffusion and advection along environmental gradient. In this model, the species are assumed to be identical except spatial variation: one lives in the heterogeneity environment, the other lives in the homogeneity environment. The main results of this paper are two fold: (i) The species living in homogeneous environment can never wipe out their competitor; (ii) Explore the condition on the diffusion and advection rates for exclusion and coexistence. It is proved that for fixed dispersal rates, when the strength of the advection is sufficiently strong, the two competitive species coexist. This is a remarkable different result with that obtained by He and Ni recently for corresponding systems without advection [X. He, W.-M. Ni, J. Differential Equations, 254 (2013), 528–546].