Study On The Properties Of The Solutions For A Two-Dimensional Attraction-Repulsion System

One of the characteristics of biology is that a microorganism or cells moves in a directional due to the stimulation of external factor,which can be called chemotaxis in biology.The Keller-Segel model which firstly describe chemotaxis is mathematical model.Chemotaxis are prevalent in biological field,so the study of Keller-Segel model or its derived model not only enrich the theoretical knowledge,but also solve some practical problems.This dissertation is devoted to dealing with the parabolic-elliptic-elliptic attraction-repulsion chemotaxis system:(?)where ? is abounded convex domain in R2 with smooth boundary,?,?,?,?,?,?>0,q?1,r?1.We study the competition among the repulsion,the attraction,the nonlinear productions to explore the properties of solutions for the two-dimensional attraction-repulsion chemotaxis system.The dissertation is divided into four chapters as follows:In Chapter 1,we mainly introduce the background and the present research conditions of Keller-Segel model and describe the main content of the dissertation.In Chapter 2,we give conditions of global existence for the two-dimensional attraction-repulsion chemotaxis system by using Young's inequality and other methods.More precisely,if q<r or q=r,??-???<0,the solutions of this model are global boundedness.In Chapter 3,we have that the nonradial solutions of the system will blow up at a finite time when the initial mass satisfy certain conditions.Moreover,We provide an explicit lower bound of blow-up time for the two-dimensional attraction-repulsion chemotaxis system by energy functions.In Chapter 4,we summarize the main results of the dissertation,and proposes some interesting problem of the thesis to be done.