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.
Vanishing Viscosity for Traffic on Networks
COCLITE, Giuseppe Maria;
2010-01-01
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.File in questo prodotto:
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