The global solution of the interaction problem for the Aw-Rascle model with phase transitions

In this paper, we discuss the interactions of elementary waves and phase boundary for traffic flows introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44(2006) 287-303]. Under the entropy conditions, we constructively obtain the existence and uniqueness of the solution. This result shows that, for some cases, a shock may speed up the increasing of the width of a free(congested) zone and a congested(free) zone may disappear into a free(congested) one. These phenomena also appear in the Kerner's observations. From the analytical point of view, this is one of the few results of the interactions of elementary waves for conservation laws developing phase transitions. Copyright (c) 2012 John Wiley & Sons, Ltd.