Traffic flow on networks : conservation laws models

The underlaying equations for the models we consider are hyperbolic systems of conservation laws in one dimension: ut + f(u)x = 0, where x ∈ R, u ∈ R and Df(u) is assumed to have real distinct eigenvalues. The main mathematical novelty is to describe the dynamics on a network, represented by a directed topological graph, instead of a real line. The more advanced results are available for the scalar case, i.e. n = 1.

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