The initial value problem of coupled Aw-Rascle traffic model with Chaplygin pressure

Abstract

This paper studies the initial value problem of coupled Aw-Rascle (CAR) traffic model with Chaplygin pressure. A definition of weak solution to CAR model is developed to obtain the waves with phase transition. Combining the waves of Aw-Rascle traffic model, we construct the solutions to the Riemann problem of CAR model with Chaplygin pressure. Without imposing additional coupling conditions, we obtain the existence, uniqueness and stability of Riemann solutions. Then we study the interaction problem of the CAR model with Chaplygin pressure, which models traffic phenomenon with careless driving in a certain section of the highway. From the solutions to the interaction problem, we can observe the formation and disappearance of traffic jam. The mathematical mechanism of traffic jam is analyzed, and the result is in good agreement with real traffic flow.