Time Behavior Analysis Of Solutions For Two Kinds Of Mathematical Biology Chemotaxis Models

In this paper,we study the large time behavior of solutions for two kinds of mathematical biology chemotaxis model.In Chapter 1,we introduce the present research background of related Keller-Segel chemotaxis model and virus infection chemotaxis model,as well as the research situation at home and abroad.In Chapter 2,we deal with the Cauchy problem of the parabolic-elliptic keller-Segel chemotaxis model where the parameters x,a,b are positive constants,k>1 and N is a positive integer.First,it is shown that this system possesses the global existence and boundedness of the classical solution(u(x,t;u0),v(x,t;u0))for the given initial function u(x,0;u0)=u0(x).Furthermore,we consider the asymptotic stability of the constant equilibrium(?)for(?)with a constant0<C<a/2?.In Chapter 3,we consider the boundedness of solutions to the following virus infection chemotaxis model with Beddington-DeAngelis type#12where ?(?)RN is a bounded domain with smooth boundary,and N is a positive integer.Here u and v stand for the population density of healthy uninfected and infected cells,respectively,and w is used to describe the concentration of virus particles.The parameters ?>0,a>0,b? 0,??0,where the parameter R is primarily thought of as being positive,Dw(v)was assumed to be an increasing function,that it,Dw(v)=D0+q(v),here D0 is a constant representing free diffusion rate of free viruses,and q(v)fulfilling q(0)=0 is an increasing function of v.Given the initial data(u0,v0,w0),it is shown that this system possesses the global existence and boundedness of the classical solution for N-1/N<?<1.In Chapter 4,we list out the leading research results of the paper and recommend further questions to be solved in the future.