The Effect Of Logistic Term On A Kind Of Density-dependent Chemotaxis Model

Chemotaxis is a common phenomenon in nature,such as a directional movement of cells in response to a chemical.It’s a kind of chemotaxis,this kind of innate reaction enables the organism to pursue the advantages and avoid the disadvantages,and adapt to the environment,therefore,the in-depth study of chemotaxis is of great theoretical significance and practical value.There is only a preliminary study on the chemotactic-consumptive model which depends on the motion of indirect signal.In this paper,we study the global existence and long-term behavior of the solution of chemotactic model with generalized Logistic term under certain conditions by means of prior estimation of the solution,ODE comparison principle and energy functional.Finally,under certain initial and boundary conditions,if l=2(n≥4)and μ is sufficiently large,or l>min{max{n/2,1},2} and μ>0,then the system has global bounded solutions.By using the energy functional,we can obtain that the global bounded solution converges to((ρ/μ)1/l-1,0,1/δ(ρ/μ)1/l-1)as t→+∞.The rate of convergence is exponential if l≥ 2,and the rate of convergence is algebraic if 1<l<2.