Mathematical Analysis Of A Predator-prey Model

This paper considers a predator-prey model.The new model considers some mix-ture of tracking prey and tracking the prey's resource,and it actually is a system of reaction-diffusion equations with self-diffusion and cross-diffusion,the model describ-ing interactions between the predator and the prey.Based on the Schauder fixed-point theorem,this paper proves the global existence,boundedness and uniqueness of a weak solution to the model by studying the well-posedness of two decoupled nonlin-ear parabolic problems associated with the original nonlinear reaction-diffusion-taxis system.