The Asymptotic Limit And Wave Interaction Problem Of The AR Traffic Flow Model Under The Logarithmic Pressure

In this paper,we mainly focus on the perturbed Riemann problem and asymptotic limit problem for the AR traffic flow model with the logarithmic pressure term,and the Riemann problem of the AR traffic flow model with the modified logarithmic pressure term at ?<e^-1.For the AR traffic flow model with the logarithmic pressure term with perturbed parameter,the construction of the Riemann solutions of the system is first given through the phase plane diagram.And then the limit behavior of the Riemann solutions of the system is analyzed by the vanishing pressure method.In particular,some numerical results are given to confirm the generated delta shock wave when the limit ??0 is taken.For the AR traffic flow model with the logarithmic pressure term without perturbed parameter,mainly by the characteristic method to analyse the characteristic of the system,so as to determine the types of possible basic waves.Then the Riemann initial value is perturbed appropriately and the global solution of the perturbed Riemann problem of the system is constructed according to the method of the wave interactions.Finally,when the perturbation parameter tends to zero,whether the limit solution of the perturbation Riemann problem is consistent with that of the corresponding Riemann problem is further discussed,so as to judge whether the system is stable or not.For the AR traffic flow model with the modified logarithmic pressure term,we mainly study the construction of the solution of Riemann problem in the case of ?<e^-1.The main arrangement of the paper is as follows:In the first chapter,the research background and current situation of AR traffic flow model are introduced.In the second chapter,the basic concepts and definitions related to this paper are given.In the third chapter,the Riemann solutions of the AR traffic flow model with the logarithmic pressure term with perturbed parameter are studied and the Riemann solutions in all cases are constructed.The limit behavior of the Riemann solutions of the system when ??0 is emphatically discussed,especially the formation of delta shock wave when u₊<u_<sub> and vacuum state when u₊>u_<sub> is discussed.And we also give some numerical results to verity the generation of the delta shock wave.In the fourth chapter,the global solutions of the Riemann problem with the three piecewise constant initial data in AR traffic flow model under the logarithmic pressure are constructed,and the interaction of various waves is discussed in detail,the emphasis is on the phenomena that may occur during the interaction of these waves.Finally,it is shown that the Riemann solutions of the system are stable for the special small perturbation of the Riemann initial values.In the fifth chapter,the AR traffic flow model under the modified logarithmic pressure is analyzed,and the Riemann solutions of the system when ?<e^-1 are constructed.