Global Boundedness In Two Biology Chemotaxis Model With Logistic Source

This paper is mainly devoted to study the global boundedness of Keller-Segel model from biology, chemotaxis is the significant feature of Keller-Segel model. Chemotaxis is a reaction which come from the stimulus of chemicals, such as near or far from the stimulus. It is the nature of the creature. Keller-Segel model plays an essential role in biology, which can explain some biology phenomenons such as cell migration, tumor growth and so on.This paper is divided into the following three chapters:Chapter 1: we introduce the background and the development of the related model.Chapter 2: we study two-species chemotaxis models with logistic source. We first construct weight function to obtain the boundedness of the solution of the model in()pL ? norm; According to the heat semigroup theory and Moser iteration, we obtained that the global solution exists and is uniformly bounded under certain conditions.Chapter 3: we study the quasilinear attraction- repulsion parabolic-parabolic –parabolic model with logistic source. By means of constructing energy function, we obtain the solution of model is global in time and uniformly bounded under some explicit conditions.