ON STEADY STATE OF SOME LOTKA-VOLTERRA COMPETITION-DIFFUSION-ADVECTION MODEL

In this paper, we study a shadow system of a two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. We show that for any given migration, if the product of interspecific competition coefficients of competitors is small, then the shadow system has coexistence state; otherwise we can always find some migration such that it has no coexistence state. Moreover, these findings can be applied to steady state of the two-species Lotka-Volterra competition-diffusion-advection model. Particularly, we show that if the interspecific competition coefficient of the invader is sufficiently small, then rapid diffusion of the invader can drive to coexistence state.