The Riemann Problem Hyperbolic Systems Of Conservation Laws

In this thesis, we will study the Riemann problem with the initial data containing Dirac delta functions for the one-dimensional zero-pressure relativistic Euler hyperbolic systems of conservation laws、the zero-pressure gas dynamics hyperbolic systems of conservation laws and the Chaplygin pressure Aw-Rascle traffic model.This thesis was divided into five chapters, in the first two chapters, we present introduction and some basic knowledge. In the third, fourth and fifth chapter, we separately consider the following systemIn the third, fourth chapter of this thesis, we respectively solve the Riemann problem with the initial data containing Dirac delta functions for the one-dimensional zero-pressure relativistic Euler hyperbolic systems of conservation laws and zero-pressure gas dynamics hyperbolic systems of conservation laws. With characteristic analysis, under suitably generalized Rankine-Hugoniot relation and entropy condition, we constructively obtain the global generalized solutions that explicitly exhibit four kinds of different structure involving delta shock waves.In the fifth chapter, we solve the Riemann problem with the initial data containing Dirac delta functions for the Chaplygin pressure Aw-Rascle traffic model. Under suitably generalized Rankine-Hugoniot relation and entropy condition, we constructively obtain the global generalized solutions that explicitly exhibit four kinds of different structure involving delta shock waves.