Global Behavior for a Diffusive Predator-Prey Model with Stage Structure and Nonlinear Density Restriction-II: The Case in R1

This paper is a continuation of Part I 1 . In Section 3 of Part I, using the energy estimate and bootstrap arguments, the global existence of solutions for a Holling type III cross-diffusion predator-prey model with stage-structure has been discussed when the space dimension be less than 6. However, to obtain the L∞ estimate for the population density w of predator species, there is not cross-diffusion for w in Part I. All diffusive predator-prey systems behave, more or less, in the same way, for both semilinear and cross-diffusive models, at least for small values of the cross diffusivities. Consequently, all the available information for linear diffusive models is essential to realize the behavior of the most complicated cross-diffusive systems 2–17 . In this paper, we consider the following cross-diffusion system: