The Delta Shock Wave Solutions And The Stability Of The Viscous Solution For The Uncoupled Hyperbolic Systems Of Conservation Laws

In this thesis,the stability of delta shock wave solution for the uncoupled hyperbolic systems of conservation laws are considered,which include the triangular type hyperbolic system and the simplified non-strictly hyperbolic system.Firstly,we study the Riemann problems for the two uncoupled hyperbolic system of conservation laws by employing the method of phase plane analysis for each Riemann initial data.The detailed Riemann solutions are constructed and then the conditions of the occurance of delta shock wave solution are determined.Finally,the stability of delta shock wave solution is studied by using the vanishing viscosity method together with the self-similar transformation method.This paper can be divided into five chapters as follows:In chapter one,we mainly introduce the related physical background for this thesis and deliver the main research methods used in this paper.In chapter two,for the basic definitions and related theorems about uncoupled hyperbolic systems of conservation laws are given respectively,which can be served as the foundation for this thesis.In chapter three,the Riemann problem for the triangular hyperbolic system of conservation laws is considered.The Riemann solutions are constructed under all kinds of Riemann conditions,which contains an excessive compression solution called as the delta shock wave.Consequently,the stability of delta shock wave solution is investigated in detail by employing the self-similar vanishing viscosity method.In chapter four,the Riemann problem for the non-strictly hyperbolic system is also studied.We first construct the solutions to this Riemann problem for all kinds of Riemann initial conditions,in which an excessive compression solution called as the delta shock wave is also contained.Then,the stability of delta shock wave solution we is also investigated by using the self-similar vanishing viscosity method.In chapter five,The problems studied and conclusions obtained in this thesis are summarized and discussed.