Riemann Problem Of Several Classes Nonlinear Hyperbolic Conservation Laws Equations

In this thesis,we will study the Riemann problem with the initial data containing the Dirac delta function for the relativistic Chaplygin Euler equations,the interactions of delta shock waves for the Aw-Rascle traffic model with split delta functions and the Riemann problem for the relativistic generalized Chaplygin Euler equations.This thesis was divided into five chapters.In the first chapter and second chapter,we present introduction and some basic knowledge,respectively.In the third,fourth and fifth chapter,we separately consider the following system(?)In the third chapter of this thesis,we study the Riemann problem with the initial data containing the Dirac delta function for the relativistic Chaplygin Euler equations.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,Moreover,we obtain the stability of generalized solutions by making use of the perturbation of the initial data.In the fourth chapter,we solve the interactions of delta shock waves for the Aw-Rascle traffic model with split delta functions.We mainly analyse the interactions between ?-shock wave and contact discontinuity when the initial data are three piecewise constant states,and we constructively obtain the solutions under four kinds of different interactions.Meanwhile,we obtain the stability of solutions when ??0.In the fifth chapter,we study the Riemann problem for the relativistic generalized Chaplygin Euler equations.We mainly analyse the formation of mechanism for ?-shock when the characteristic fields are genuinely nonlinear,under suitably generalized Rankine-Hugoniot relation and entropy condition,we constructively obtain the global generalized solutions involving delta shock waves.