Boundedness Of Solutions To A Chemotaxis Model With Nonlinear Chemotactic Sensitivity Terms

In recent years,Chemotaxis in biology has been described as a class of partial differential equation,and perform qualitative and quantitative analysis.In particular,the existence,boundedness,and large-time behavior of the solution of the biological chemotaxis model have received more and more attention.In the present paper we consider a kind of biological Chemotaxis model with nonlinear chemotactic sensitivity function with indirect signal production and nonlinear chemotactic sensitive function,where ?? Rn represents the bounded region with smooth boundary (?)?,for any s?1,the chemotactic sensitive function f(s)? cs?,where c>0 and ?<2/nThis paper is mainly developed from the following sections:The first chapter:Briefly introduces the biological background of biological chemotaxis models,overseas and domestic research status,and the main contents of this paper.The second chapter:Mainly introduces some basic lemmas needed in the proof process of the main conclusions proving.The thirdly chapter:The local existence of the solution to the model was proved by the operator semigroup theory and the contraction mapping theory,and the uniqueness of the solution to the model was shown by the energy method.The fourth chapter:The uniform boundedness of the solution are proved by energy estimation and Moser iterative method.The fifth chapter:Summarizes and prospect.