Population dynamics in a reaction-diffusion-advection predator-prey model with Beddington-DeAngelis functional response

In this paper, we consider a two-species predator-prey model in advective heterogeneous environments with the Beddington-DeAngelis interaction term, where the Danckwerts boundary conditions are imposed. Applying the comparison principle for predator-prey system and persistence theory, we draw a clear picture on the long-time dynamics, which also indicates the existence and non-existence of the coexistence steady state solutions. Specially, the uniqueness of the coexistence steady state solutions is considered under certain conditions.