The Research Of The Aw-Rascle Traffic Flow Model

This paper is concerned with the traffic light problems in traffic flow and the generalized δ-entropy condition to the Riemann solutions to the traffic flow Aw-Rascle model for Chaplygin gas and the Riemann problem to the transport equations with delta initial data.Chapter 2 given some fundamental notations and concepts for the hyper-bolic conservation laws, and introduce some general theories for one dimensional hyperbolic conservation laws, which will be useful to the following contents.Chapter 3 is devoted to investigating the traffic flow controlled by traffic light on a unidirectional roadway. The traffic light problems are governed by the Aw-Rascle model and some traffic rules:cars must stop in the red period and do not smash into one another. We show the evolution of the traffic flow of the cars moving through traffic light that turn on and off with a specific frequency. The criterion for whether the shock gets through the traffic light is obtained. For the shock to get through and the light to operate freely, the green period must exceed the critical value tc. Furthermore, we prove that the quantity of traffic flow attains its maximum at the traffic light. Some numerical simulations are given, which coincide with the theoretical results and traffic flow.Chapter 4 studies the generalized δ-entropy condition to the Riemann so-lutions to the Aw-Rascle model in traffic flow for Chaplygin gas. We construct the solutions globally under the generalized Rankine-Hugoniot relations and the δ-entropy conditions and generalized δ-entropy conditions. A new kind of delta wave which is called a primary delta wave is defined in some solutions. The primary delta wave satisfies the generalized Rankine-Hugoniot relations and gen-eralized δ-entropy conditions. It generates initially from the delta initial data, which either evaluates a delta wave which weight becomes strong and strong or disappears at a finite time.Chapter 5 studies the Riemann problem to the transport equations with delta initial data. We construct the solutions globally under the generalized Rankine-Hugoniot relations and the δ-entropy conditions. Furthermore, by using of the perturbation of the initial data, we obtain the stability of generalized solutions.