Limit Behavior Of Riemann Solutions To The Multi-Pressure Aw-Rascle Model

Aw-Rascle model is an important hydrodynamic system in traffic flow,which is widely used to describe traffic problems such as the formation of traffic jams on roads.Based on the general characteristics of real traffic conditions,this thesis studies the Riemann problem and the limit behavior of Riemann solution for the multi-pressure Aw-Rascle model.The first chapter,we introduce the traffic flow model and the research status of the delta shock wave,and briefly describe the research work of this thesis.The second chapter,the delta-shock and vacuum solution of the zero-pressure flow system are introduced.The third chapter,we solve the Riemann problem for the multi-pressure Aw-Rascle model with the help of characteristic and phase plane analysis method,three kinds of Riemann solutions are constructed,and then the limit of Riemann solutions is studied when several pressure parameters tend to zero.It is shown that the limit of the solution of the multi-pressure Aw-Rascle model is not the entropy solution of the zero-pressure flow system.On the basis of the third chapter,the Riemann problem of the multi-pressure AwRascle model with a perturbation and its Riemann solutions are studied in Chapter 4.The limit of the Riemann solutions is analyzed when several pressure parameters tend to zero.It is observed that the solution of the perturbed multi-pressure Aw-Rascle model converges to the entropy solution of the zero-pressure flow system.