The Existence Of Global Solutions For A Class Of Chemotaxis System With Generalized Logistic Source

Chemotaxis is a directional migration strategy of cells to chemical substances.This innate ability enables organisms to learn to seek advantages and avoid disadvantages and adapt to the environment.Hence,it has great theoretical significance and practical value to study chemotaxis deeply.In this paper,the global existence and large time behavior of solutions for a class of chemotaxis system with generalized Logistic source(?)are studied via some priori estimates,the comparison principle of ODE and the construction of free energy,etc.In Chapter 1,the preface mainly introduces the research background and research present situation of chemotaxis,and finally leads to the main research content of this paper.In Chapter 2,we consider the global boundedness of the above chemotaxis model with general Logistic term.We prove some prior estimates of the unknown functionsandon the basis of the existence of local solutions,then we obtain that there exists a constant>0 such that(?)for all t>0.Finally,the global classical solution of the above system is obtained.In Chapter 3,we study the large time behavior of the above chemotaxis model with general Logistic term.In the case of0,through the comparison principle of ODE and contradiction method,it is concluded that(?).In the case of >0,the large time behavior of the solution can be obtained by constructing the free energy.Moreover,we show that the solution of above system will converge to the spatially equilibrium(?).