Cauchy Problem For Aw-Rascle Traffic Flow Model

Aw-Rascle traffic flow model can be used to study the situation of the road traffic jams. It is the basis of the single road network model, the multi-lane traffic flow model and the mixed traffic flow model. It has attracted extensive attention from many scholars. This thesis is mainly focused on Cauchy problem of the Aw-Rascle traffic flow model. It consists of two parts.In the first part we study the Cauchy problem of the classical Aw-rascle traffic flow model. At first, under hypotheses of continuous and piecewise smooth initial values, with the help of characteristic analysis and uniformly a priori estimate, we prove that, as there is no vacuum at the initial time, the vacuum never develops in solutions. We also obtain the existence and uniqueness of smooth solution for a kind of Goursat problem in a angle region. Furthermore, we show that the Cauchy problem possesses a unique global continuous and piecewise smooth solution. Next, we give bounds of the life span of classical solutions.In the second part we consider the cauchy problem of the modified Chaplygin type of Aw-Rascle traffic flow model. With some suitable assumptions of initial data, the existence and uniqueness of global smooth solution as well as continuous and piecewise smooth solution of the Cauchy problem is shown, respectively. The corresponding results for Chaplygin gas and generalized Chaplygin gas pressure law are also obtained. In addition, we also estimate the life span of classical solutions.