Existence And Stability Of Traveling Waves Of A Generalized Chemotaxis Model With Logarithmic Sensitivity

This dissertation is mainly concerned with the existence and stability of travelling wave solutions of a generalized chemotaxis model with logarithmic sensitivity.It is divided into three chapters.The chemotaxis phenomenon,background and recent developments on travelling waves solutions of the chemotaxis model are introduced in Chapter1.Main results of the existence and stability of traveling waves are then presented.In chapter 2,a system of viscous conservation laws is constructed with the Hopf-Cole transformation(HCT)on the chemotaxis model.The existence and decay rate at infinity of the traveling wave solutions are then proved by the phase plane analysis for the transformed model.The existence and decay rate of the travelling waves of the chemotaxis model is finally obtained with the HCT.In chapter3,the nonlinear asymptotic stability of the travelling waves for the transformed model is proved by the energy method,and thus is also true for the original model.The novelty of the present results obtained in this dissertation is the existence and stability of travelling wave solutions for the generalized chemotaxis model.