GLOBAL ENTROPY SOLUTIONS AND ZERO RELAXATION LIMIT FOR GREENBERG-KLAR-RASCLE MULTILANE TRAFFIC FLOW MODEL

We construct the global bounded variation (BV) solutions and investigate the zero relaxation limit of the Greenberg-Klar-Rascle multilane model of traffic flow. The model is governed by a 2 × 2 Temple system with a discontinuous relaxation term. The system is marginally stable. Under such circumstances, there is no invariant region for this system. Instead, we consider two sequences of time evolution regions for free and congested flow cases. The global existence of entropy solutions to the Cauchy problem of the multilane model is established by a new version of the generalized Glimm scheme for some suitable class of initial data. We prove that the total variation of the solutions is bounded for all time if the total variation of the initial data is finite. We find that the Lipschitz constants in time for the L¹_loc norms of the solutions are independent of the relaxation parameter, which enables us to get the zero relaxation limit.