Vanishing Viscosity for Traffic on Networks

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 so...

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Bibliographic Details
Published inSIAM journal on mathematical analysis Vol. 42; no. 4; pp. 1761 - 1783
Main Authors Coclite, G M, Garavello, M
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2010
Subjects
Approximation
Conservation laws
Mathematical analysis
Mathematical models
Networks
Roads
Studies
Traffic engineering
Traffic flow
Viscosity
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Summary: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. [PUBLICATION ABSTRACT]
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ISSN:0036-1410
1095-7154
DOI:10.1137/090771417