Properties Of The Solutions To Two Chemotaxis Systems With Logisitic Source

The global existence is a very important problem in the theoretical study of partial differential equations.This paper studies the global existence and boundedness of solutions of two biological chemotaxis systems,which are mainly divided into the following three chapters:The first chapter is preface,which mainly introduces the biological background of chemotaxis system,the development status of some chemotaxis models at home and abroad and the main research content.The second chapter mainly studies the properties of the solution of oxygen-consuming chemotaxis systems with logistic source term(?u-?u~2)Through a series of prior estimates,we can prove that when the parameters of the chemotaxis equations satisfy certain conditions,the initial boundary value problem of the chemotaxis equations has a unique bounded classical solution.In chapter 3,the Neumann initial-boundary value problem of oxygen-consuming chemotaxis equations with logistic source term(?u-,?u~?)is studied In contract to the second chapter,we mainly prove that as long as the nonlinear growth indicator ?>7/3,for any ??(?),?>0,there exists a global bounded classical solution.