On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flowSur une fermeture des équations de conservation de la masse et l'analyse de la stabilité dans la théorie mathématique de la circulation véhiculaire

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow. To cite this article: V. Coscia, C. R. Mecanique 332 (2004).