Riemann Problem Of Nonlinear Hyperbolic Conservation Laws Systems

In this thesis,we will study the Riemann problem with the initial data for the nonsymmetric Keyfitz-Kranzer system with Chaplygin pressure,vanishing pressure limit of solutions to the Aw-Rascle model for generalized Chaplygin gas and delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas.This thesis was divided into five chapters.In the first chapter present introduction,second chapter present some basic knowledge.In the third chapter consider the Riemann problem with the initial data containing the Dirac delta function for the nonsymmetric Keyfitz-Kranzer system with Chaplygin pressure.Under the generalized Rankine-Hugoniot conditions and entropy condition,we constructively obtain the global existence of generalized solutions including delta shock waves that explicitly exhibit four kinds of different structures.Moreover,we obtain the stability of generalized solutions by making use of the perturbation of the initial data.In the fourth chapter consider the Riemann problem for the Aw-Rascle traffic with the generalized Chaplygin gasThe existence and uniqueness of ?-shock waves are established under the generalized Rankine-Hugoniot conditions and entropy condition.The delta shock may be useful for description of the serious traffic jam.More importantly,it is proved that the limits of the Riemann solutions of the Aw-Rascle traffic model are exactly those of the pressureless gas dynamics system with the same Riemann initial data as the traffic pressure vanishes.In the fifth chapter the Riemann solutions for the relativistic Euler equations for generalized Chaplygin gasIt is rigorously proved that,as the pressure vanishes,they tend to the two kinds of Riemann solutions to the zero pressure relativistic Euler equations,which include a delta shock formed by a weighted ?-measure and a vacuum state.