The Study Of The Riemann Solutions For Aw-Rascle Model And Pressureless Euler System

Firstly,this paper investigates the interaction of elementary waves and the vanishing pressure limit of Riemann solutions of AW-Rascle model for modified Chaplygin gas.Secondly,this paper proves the stability of Riemann solutions for the pressureless Euler system with the Coulomb-like friction term.Chapter 1 presents the physical background and research status of Aw-Rascle mod-el,transport equations,pressureless Euler system with the Coulomb-like friction term,modified Chaplygin gas and vanishing pressure method.Chapter 2 considers the Riemann solution and the interaction of elementary wave for the traffic flow model proposed with the modified Chaplygin gas pressure law.Firstly,under the Rankine-Hugoniot relation and the entropy condition,we constructively obtain the global Riemann solution by the analysis method in characteristic and phase plane.The Riemann solutions consist of R + J or R + J according as the different data ranges of the initial data.Furthermore,with these results of Riemann problem,we have four cases according as the different combinations of elementary waves as following:R+ J and R+ J;R + J and S + J;S + J and R+ J;S + J and S + J when the initial data consist of three pieces of constant states.Moreover,let the perturbed parameter ? tends to zero,we have proved the stability of the Riemann solutions.Chapter 3 studies the formation of the ?-shock wave and the vacuum state in the Riemann solution of the Aw-Rascle model for the modified Chaplygin gas are studied as the pressure vanishes.And the strength and the propagation speed of the ?-shock wave are described in detail.As the pressure vanishes,the Riemann solution containing two shock waves converges to a ?-shock solution.However,the strength and the propagation speed of the ?-shock in the limit situation are different from the transport equations.This phenomenon is analyzed.By contrast,any two-rarefaction-wave Riemann solution is shown to tend to the vacuum solution to the transport equations.Chapter 4 proves the stability of Riemann solutions for the pressureless Euler system with the Coulomb-like friction term.Given an initial Riemann disturbance containing three states,We prove that when ?0,u0 is constant in the initial condition,the Riemann solutions for the pressureless Euler system with the Coulomb-like friction term is stable.