The Riemann Solution Of Non-strictly Hyperbolic Conservation Laws For Stability Analysis With Self-similar Viscosity Method

In this paper, our main purpose is to consider the stability of Riemann solution for the system of non-strictly hyperbolic conservation laws, in which we use the viscosity vanishing method and self-similar transformation. First, we consider the viscous regularization of delta shock wave solution for a simplified chromatography system. In the case of-1<v_<0<v the solution of the simplified chromatography system is a delta shock wave. We take the viscosity vanishing method to consider the solution when the viscosity tend to zero, and use self-similar transformation to investigate the existence of the solution. Then we consider the delta standing wave solution for the linear scalar conservation law with discontinuous coefficients using a self-similar viscous regularization. In the case of k+<0<k, the solution of the equation is a delta standing wave. Similarly, we can also take the viscosity vanishing method to consider the solution when the viscosity tend to zero, and use self-similar transformation to investigate the existence of the delta standing wave.This thesis can be divided into five chapters.The first chapter introduces the related background for the non-hyperbolic conservation laws system.The second chapter is the basic knowledge which is the foundation of this thesis.The third chapter is mainly concerned with the viscous regularization of delta shock wave solution for a simplified chromatography system.The forth chapter is devoted to the delta standing wave solution for the linear scalar conservation law with discontinuous coefficients using a self-similar viscous regularization.In the fifth chapter, we make a summary and outlook to the contents of this dissertation.