Global solution for a general cross-diffusion two-competitive-predator and one-prey system with predator-taxis

This paper is concerned with a general cross-diffusion system modeling the population dynamics of two-competitive-predator and one-prey with predator-taxis. Firstly, through the use of contraction mapping principle, the Schauder estimates and Lp-estimates of parabolic equations, we investigate the local existence and boundedness of the unique classical solution for this system. Furthermore, the global existence and uniqueness of classical solution for this system are obtained base on some priori estimates. Finally, several numerical simulations are presented to demonstrate the effects of the predator-taxis to the population dynamics and support the theoretical results. The novel point of this work is that, in addition to the self-diffusion of one predator species, the cross-diffusion not only between predator and prey (predator-taxis) but also between two predator species (compete for available resources) are considered.