Formation Of Delta-shocks For Aw-Rascle Model With General Pressure

The Aw-Rascle model in traffic flow is an important type of hyperbolic conservation law equations,which has important applications in both fluid dynamics and practical transportation problems.This thesis mainly studies the delta shock wave and its formation mechanism for the Aw-Rascle model with general pressure.The first chapter,we introduce the research background and situation of the AwRascle traffic flow model.The second chapter,we review the delta shock wave and vacuum solution of the transport equations.The third chapter,we solve the Riemann problem for the Aw-Rascle model with general pressure,and obtain the Riemann solutions of three different structures involving delta shock waves.It is proved that,as the pressure disappears,any delta-shock solution and Riemann solution including shock wave and contact discontinuity for this system converge to the delta-shock wave solution to the transport equations;any Riemann solution including rarefaction wave and contact discontinuity converges to the vacuum solution to the transport equations.The fourth chapter,we consider the general-pressure Aw-Rascle model with a flux perturbation.Firstly,the Riemann problem of this model is solved,Riemann solutions of three different structures including parameterized delta shock wave are constructed.Secondly,it is shown that,when the flux perturbation disappears,any parameterized delta-shock solution for the general-pressure Aw-Rascle model with a flux perturbation tends to the delta-shock solution of the the Aw-Rascle model with general pressure.Finally,it is analyzed that,when the pressure and flux perturbation disappear at the same time,any parameterized delta-shock solution and Riemann solution including shock wave and contact discontinuity for the general-pressure Aw-Rascle model with a flux perturbation tends to the delta-shock solution of the transport equations;any Riemann solution containing rarefaction wave and contact discontinuity tends to be the vacuum solution of the transport equations.