Large Time Behaviour for a Prey-Taxis System

Abstract

The large time behaviour for a more general prey-axis system is considered. The asymptotically uniform boundedness of solutions in a suitable space is derived to ensure the dissipativity of the system. Based on the dissipativity of the system, the existence of a global attractor is obtained. The main technique used in this paper is the $L^{p}-L^{q}$ estimation method.