Asymptotic Stability Of A Composite Wave Of Two Traveling Waves To A Generalized Parabolic-hyperbolic System

This dissertation is mainly concerned with the asymptotic stability of a composite wave for a generalized parabolic-hyperbolic system.It is divided into three chapters.The chemotaxis phenomena,background and recent de-velopments on travelling waves solutions of the chemotaxis models are introduced in Chapter 1.Main results of the existence and nonlinear stability of composite waves are then presented for the model.In chapter 2,a system of conservation laws is constructed by using the Hopf-Cole transformation on the original chemotaxis model.Then under some appropriate assumptions on f,we obtain the composite wave solution of parabolic-hyperbolic system and their exponential decay rates at infinity.In chapter 3,under further appropriate assumptions on f,the weighted energy method is then applied to prove the nonlinear stability of composite wave when the ini-tial perturbation is small in H~1norm.There have been a lot of important works on the stability of traveling waves to chemotaxis models,our stability results about the composite wave generalize the corresponding results ob-tained in related references.