Global Dynamics of Two-species Lotka-Volterra Competition-diffusion-advection System with General Carrying Capacities and Intrinsic Growth Rates

We study a Lotka-Volterra competition-diffusion-advection system with general intrinsic growth rates and carrying capacities for two competing species in heterogeneous closed environments, where individuals are exposed to unidirectional flow (advection) but no individuals pass through the boundary. Firstly, we establish the classification of linear stability for the two semi-trivial steady states. Then, we rule out the existence of co-existence steady state under some special conditions, which seems non-trivial and new. Combining these two aspects with the theory of monotone dynamical systems, we prove the main results (Theorem 1.1). Our results suggest that the spatial distributions of carrying capacities and intrinsic growth rates totally change the "evolutionary stability strategy of species". Precisely, if the carrying capacities increase fast, then "slower diffuser always prevails"; if the carrying capacities increase slow, then "faster diffuser always prevails"; if the carrying capacities increase intermediately, then two species coexist.