Qualitative Analysis Of Solutions For Multi-species Chemotaxis System

The study of chemotaxis model is of great significance to the development of mathematics and biology.This paper mainly studies the properties of the solutions for three kinds of multi-species chemotaxis models,including the existence,boundedness and asymptotic behavior of the solutionsFirstly,the initial boundary value problem of a two-species quasilinear chemotaxis model with logistic growth term is studied in this thesis.This model describes the chemotaxis of cells or microorganisms under the combined action of chemical attraction signal,nonlinear diffusion,chemotaxis sensitivity related to the concentration of the signal substance and logistic growth term.The local existence of the solution of the model is proved by the nonnegative qualitative analysis of the coefficient matrix.Based on the maximal Sobolev regularity and some common inequalities,it is shown that this system possesses a unique global bounded classical solution provided that the logistic growth coefficients ?1,?2 are suff-iciently largeSecondly,the initial boundary value problem of a chemotaxis model with diffusion term and chemotactic sensitivity is studied.The model describes the nonlinear diffusion with chemotactic sensitivity functions depend on two-species densities.The local existence of the model is proved,then by energy estimation and analytical techniques it is proved global existence and uniform boundedness of solution in two casesFinally,two-species chemotaxis model with two chemicals is studied.Firstly,in the two-dimensional case,where the conditions |x'i|(i=1,2)are bounded,the energy estimation is used to prove that the model has a unique global bounded classical solution;If the dimension n?3,the model exists a unique globally bounded classical solution provided that ?1,?2 are sufficiently large.In particular,for the first time,an accurate result when ?i0>0 is obtained in this case ?i>?i0,there is no blowup in the model.In addition,by constructing appropriate energy functional,it can be obtained the asymptotic behavior of the solution in three different competitive situations.