Global Attractor for a Chemotaxis Model with Reaction Term

This paper deals with global attractor of a quasilinear parabolic system introduced in [1] by Horstmann and Winkler to model chemotaxis. Chemotaxis phenomenon is quite common in biosystem.The survival of many organisms, from microscopic bacteria to the largest mammals, depends on their ability to navigate in a complex environment through the detection, integration, and processing of a variety of internal and external signals. This movement is crucial for many aspects of behavior, including the location of food sources, avoidance of predators, and attracting mates. The ability to migrate in response to external signals is shared by many cell populations. The directed movement of cells and organisms in response to chemical gradients is called chemotaxis. The classical chemotaxismodel has been extensively studied in the last few years (see [1–5]); Payne and Straughan [4] tackle precise nonlinear decay for classical model. Decay for a nonlinear chemotaxis system modeling glia cell movement in the brain is treated by Quinlan and Straughan [5]. In this paper, we are concernedwith the following chemotaxis model: