We consider a Lotka-Volterra competition-diffusion-advection system with the total resources for two competitors fixed at the same level. We reveal the combined effect of competition abilities and spatial variations on the coexistence of two competing species. It is obtained that when the ratio of advection rate α to diffusion rate d1 is appropriately large, the two competing species will always coexist if the inter-specific competition coefficients (b,c) in (0,1]×(0,1] and when the ratio is appropriately small, the two species will coexist if the inter-specific competition coefficients c is appropriately small and b is in (0,1].
Keywords: coexistence; competition-diffusion-advection; linearly stable; monotone dynamical system; principle eigenvalue.