Global existence of classical solutions to the cross-diffusion three-species model with prey-taxis

This paper deals with the cross-diffusion three-species model with prey-taxis incorporating Beddington-DeAngelis response under homogeneous Neumann boundary condition. In addition to random diffusion, the predators and preys have cross-diffusion and prey-taxis during the process of interaction. By applying the contraction mapping principle, the Hölder continuity, the parabolic Schauder estimates and parabolic Lp estimates, we prove that there exists a unique global classical solution of this system.