Global solutions for a general predator-prey model with prey-stage structure and cross-diffusion

Abstract

In this paper, a cross-diffusion predator-prey model with
general functional response and stage-structure for the prey is analyzed. The global existence of classical solutions to the system of strong coupled reaction-diffusion type is proved when the space dimension less than ten by the energy estimates and the bootstrap arguments. The model and mathematical results in [ S. M. Fu, L. Zhang, P. Hu, Global behavior of solutions in a Lotka-Volterra predator-prey model with prey-stage structure, Nonlinear Anal. RWA 14 (2013) 2027-2045.] are generalized. The crucial point of the proof is to deal with the cross-diffusion term and the nonlinear predation term .