Global Existence in a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism

Abstract

One of the fundamental processes in ecology is the interaction between predator and prey. Predator-prey interactions refer to the relative changes in population density of two species as they share the same environment and one species preys on the other. There are many studies global existence or blow-up of solutions on the predator-prey model. Our this paper related to the predator-prey model with nonlinear indirect chemotaxis mechanism under homogeneous Neumann boundary conditions. We establish the global existence and boundedness of classical solutions of our problem by using parabolic regularity theory. Namely, firstly we show that u and υ boundedness in L^p for some p>1, then we obtain the L^∞-bound of u and υ by using Alikakos-Moser iteration. Thus, it is proved that the model has a unique global classical solution under suitable conditions on the parameters in a smooth bounded domain.