A free boundary problem of a predator–prey model with advection in heterogeneous environment

This paper is concerned with a system of reaction–diffusion–advection equations with a free boundary, which arises in a predator–prey ecological model in heterogeneous environment. The evolution of the free boundary problem is discussed. Precisely, we prove a spreading–vanishing dichotomy, namely both prey and predator either survive and establish themselves successfully in the new environment, or they fail to establish and vanishes eventually. Furthermore, when spreading occurs, we obtain an upper bound of the asymptotic spreading speed, which is smaller than the minimal speed of the corresponding traveling wave problem.