Abstract:In this paper, we focus on the existence of positive solutions of a reaction-diffusion predator model with advection term. This model can be used to describe the relationship between the predator species and the prey pecies with the tendency that predators choose to hunt away from the high-density area of prey species. Based on a priori estimate for the positive solutions, the non-existence of positive solutions with respect to the growth rate of both species is estabished by using the eigenvalue theory and homogenization theory. Then the existence of positive solutions for different parameter conditions is established by using the bifurcation theory.
