Properties Of The Solutions To Two Chemotaxis Systems With Two-species

Chemotaxis is the directional movement of cells or organisms according to the concentration of chemicals in the environment.It is widely used in biology,medicine,agricultural ecology and other fields.In recent years,the chemotaxis system with multiple species has been extensively studied by scholars.We study the global existence and boundedness of the solutions to two chemotaxis systems with two species in this thesis,which is divided into the following chapters:The first chapter introduces the biological background of chemotaxis system and the research progress of some chemotaxis systems with multiple species.In the second chapter,we study the Neumann initial-boundary value problem of a two-species chemotaxis system with singular sensitivity:In this chapter,we establish the global existence of the classical solution of this problem under certain assumptions on χ1,χ2,μ1,μ2,α,β.In the third chapter,we study the Neumann initial-boundary value problem of a two-species chemotaxis system with nonlinear diffusion:In this chapter,it is shown that for any m,n>1,the problem admits a global bounded weak solution.