We prove the well-posedness of a system of balance laws inspired by [H. Holden and N. H. Risebro, SIAM J. Math. Anal., 51 (2019), pp. 3694-3713], describing macroscopically the traffic flow on a multilane road network. Motivated by real applications, we allow us for the the presence of space discontinuities both in the speed law and in the number of lanes. This allows us to describe a number of realistic situations. Existence of solutions follows from compactness results on a sequence of Godunov's approximations, while L\bfone -stability is obtained by the doubling of variables technique. Some numerical simulations illustrate the behavior of solutions in sample cases.
Goatin, P., Rossi, E. (2019). A multilane macroscopic traffic flow model for simple networks. SIAM JOURNAL ON APPLIED MATHEMATICS, 79(5), 1967-1989 [10.1137/19M1254386].
A multilane macroscopic traffic flow model for simple networks
Rossi, E
2019
Abstract
We prove the well-posedness of a system of balance laws inspired by [H. Holden and N. H. Risebro, SIAM J. Math. Anal., 51 (2019), pp. 3694-3713], describing macroscopically the traffic flow on a multilane road network. Motivated by real applications, we allow us for the the presence of space discontinuities both in the speed law and in the number of lanes. This allows us to describe a number of realistic situations. Existence of solutions follows from compactness results on a sequence of Godunov's approximations, while L\bfone -stability is obtained by the doubling of variables technique. Some numerical simulations illustrate the behavior of solutions in sample cases.
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