Global Boundedness Of Solutions To Two Kinds Of Chemotaxis Models With Density-Dependent Motility

In recent years,many researchers have modeled complex biological phenomena in nature by partial differential equations(groups),studied various properties of the equations(groups)solutions with relevant mathematical theories,and then reasonably explained and predicted biological phenomena by the properties of the solutions,such as biological chemotaxis,species competition and predation phenomena.This use of mathematical method to deal with problems with biological background,promoted the formation and development of biological mathematics.This thesis deals with the properties of solutions of a parabolic-elliptic-parabolic chemotaxis model with densitydependent motility and a predator-prey chemotaxis model with density-dependent motility,we prove the model possesses a globally bounded classical solution.This thesis mainly contains the following four sections.In Section 1,introduction.This chapter mainly introduces the research background and research status of two chemotaxis model,and briefly describes the mainly research work of this thesis.In Section 2,considering a parabolic-elliptic-parabolic chemotaxis model with density-dependent motility under zero Neumann boundary conditions.Based on the energy estimates and Moser iteration,we prove the solution of the model is global existence and uniform boundedness when the motility function satisfies the appropriate conditions.In Section 3,studying the Neumann initial boundary value problem of a predatorprey chemotaxis model with density-dependent motility.Suppose that the initial data and the parameters satisfy suitable conditions,by constructing the energy function and using Moser iteration,we prove that the above problem has a unique global bounded classical solution in two dimension bounded convex domain under some suitable conditions on the motility function.In Section 4,Summarizing the main content of this thesis and look forward to the future research work.