Time Behavior Analysis Of Solutions To Two Types Of Biological Chemotaxis Modles With Singular Sensitivity

This paper is concerned with the initial boundary value problems of two kinds of biological chemotaxis modles with singular sensitivity,including the large time behavior and the global existence of the solutions.This thesis is divided into the following four chapters:In chapter 1,we mainly introduce the biological background and research status of chemotaxis model,and briefly state the main contents of this paper and introduce some commonly used inequalities.In chapter 2,we deal with the following chemotaxis system with singular sensitivity and logistic source under non-flux boundary condition where Ω(?)Rn(n≥2)is a smooth bounded convex domain and parameters χ>0,r>0,μ>0,k>2.This chapter is mainly based on the global boundedness of solutions by Zhao and Zheng(2019),and we prove that if where δ0 is the lower bounder of v,then the solution of this system(u,v)to expon-entially converge to(?)as t→∞ in the L∞(Ω)sense.In chapter 3,we consider the model of chemotaxis-consumption with singular sensitivity under homogeneous Neumann boundary condition in a smooth bounded domainΩ(?)Rn(n≥1),parameters r>0,μ>0,k>1.Supposed that f(u)satisfies 0<f(u)≤δ(u+1)γ with some δ>0 and γ<2.It is shown that for any sufficiently smooth initial data,the above system admits a global classical solution when either n=1 and γ<2 or n≥2 and γ<1-n/4.In chapter 4,we summarize the main contents and conclusions of the thesis,and put forward several questions worth studying in the future.