Properties Of Solution For Some Chemotaxis Systems With Generalized Damping Sources

The research for chemotaxis models is of great significance to related biological phenomena,which provides rigorous theoretical analysis to explain the complex practical problems.In this thesis,we mainly study the properties of the solutions like,boundedness,asymptotically stability and the arbitrarily large concentration behavior,to the chemotaxis system with Lotka-Volterra competitive source terms,the quasilinear parabolic-parabolic chemotaxis model,the chemotaxis model with indirect chemical signal production,and the fully-parabolic two species chemotaxis model with nonlocal source terms.This thesis is divided into the following six chapters:In Chapter 1,we first briefly introduce the biological background of chemotaxis model and the research status to related models,then we introduce the main results of this thesis,and briefly summarize our innovations.In Chapter 2,we investigate the arbitrarily large concentration behavior of a parabolic-parabolic-elliptic chemotaxis model with Lotka-Volterra competitive source term,that is,By applying the viscosity vanishing method and establishing the well-posedness and finite time blow-up results for the corresponding hyperbolic-hyperbolic-elliptic model,we can obtain an unbounded phenomenon for the above chemotaxis model,that is,under some assumptions on parameters,for the radial symmetry initial values and arbitrarily large number M,one can find some points t0?(0,Tmax)and x0?? such that the solution of the model satisfy u(x0,t0)+v(x0,t0)>M.Because of the arbitrariness of the number M,the above conclusion is usually called arbitrarily large concentration behavior or transient growth phenomenon.In Chapter 3,we study the following parabolic-parabolic quasilinear chemotaxis model,For any bounded region with smooth boundary,we find a sufficient conditions such that the solution for the corresponding system possesses the phenomenon of arbitrarily lager densities.In Chapter 4,for the following chemotaxis model with indirect signal production,we study the emergence of lager densities behavior of the solution in the two cases:?1=?2=0,d2>0 and ?1,?2>0,d2?0.It is worth noting that for the corresponding parabolic-elliptic-elliptic model,we use viscosity vanishing method and some compactness arguments to obtain the local existence and uniqueness of the strong W1,q-solutions of the corresponding hyperbolic-elliptic-elliptic model.However,due to the existence of indirect signal production mechanism,we can not get the finite time blow-up for the strong W1,q-solution,this is a different result with the classical Keller-Segel model,this challenge requires us to find some new analytical techniques.In Chapter 5,we consider the following two species chemotaxis model with nonlocal competition terms,For any space dimension and the initial value,we obtain the global boundedness of solution for the system under some assumptions on parameter.On this basis,we continue to study the asymptotically stability of the system under the weak and the strong symmetric competition cases.In Chapter 6,the results of this thesis are summarized,and the possible future work is prospected.