We consider the vanishing viscosity approximation of the traffic model, proposed by Lighthill, Whitham, and Richards, on a network composed by a single junction with n incoming and m outgoing roads. We prove that a solution of the parabolic approximation exists and, as the viscosity vanishes, the solution of the parabolic problem converges to a solution of the original problem.
Coclite, G., Garavello, M. (2010). Vanishing viscosity for traffic on networks. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 42(4), 1761-1783 [10.1137/090771417].
Vanishing viscosity for traffic on networks
GARAVELLO, MAURO
2010
Abstract
We consider the vanishing viscosity approximation of the traffic model, proposed by Lighthill, Whitham, and Richards, on a network composed by a single junction with n incoming and m outgoing roads. We prove that a solution of the parabolic approximation exists and, as the viscosity vanishes, the solution of the parabolic problem converges to a solution of the original problem.
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