The Existence of a Free Boundary Problem for the Predator-Prey Model with Fear Effect

In this paper, we investigate a free boundary problem for the predator-prey model with fear effect and Beddington-DeAngelis response function in one space dimension. This system models the expanding of predator and prey species in which the free boundaries represent expanding fronts of the predator and prey species and are described by Stefan-like condition. We prove the global existence and the uniqueness of the solution.