Global Existence And Behavior In An Attraction-repulsion Chemotaxis System

Keller-Segel model is a computational and modelling way to describe chemotaxis which is a prevalent mechanism in biology. The study of Keller-Segel model and its deformation possess both theoretical and realistic significance.In this paper, we mainly study a class of attraction-repulsion model which was proposed to describe the aggregation of microglia.In Chapter 1, we mainly introduce the background of Keller-Segel model, and the research status of some specific attraction-repulsion models at home and abroad.In Chapter 2, we deal with a parabolic-parabolic-parabolic attraction-repulsion chemotaxis system. We assert that the solution of the above system is globally bounded and converges to a stationary solution under some smallness condition on initial data.In Chapter 3, we consider a parabolic-elliptic-elliptic attraction-repulsion chemotaxis system. The global solvability of the system is also established under appropriately assumptions for parameters and for small initial mass.