Dynamics of a predator-prey system in open advective heterogeneous environments

In this paper, we investigate the effect of dispersal and advection on the dynamics of a predator-prey model. More precisely, we show that the linear stability of the semi-trivial steady state is determined by the dispersal rate, the mortality rate of the predator and the advection rate. We point out that compared to homogeneous intrinsic growth rate and carrying capacity, the case in this paper is more complicated. This work gives a investigation to an open problem proposed by Nie et al. in \cite{NWW} by considering a more general model, and then, can be seen as a further development of their work \cite{NWW}.