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Critical analysis and perspectives on the hydrodynamic approach for the mathematical theory of vehicular traffic. (English) Zbl 1185.35293

Summary: This paper deals with a review and critical analysis on the modelling by hydrodynamic equations by taking into account not only the mechanistic behavior of the vehicles, but also the psycho-mechanic interactions between drivers and vehicles, with the aim of proposing various hints for research perspectives in view of further developments focused on vehicular traffic flow and conceivable developments in the dynamics of pedestrian crowds.

MSC:

35Q90 PDEs in connection with mathematical programming
35Q30 Navier-Stokes equations
76M99 Basic methods in fluid mechanics
90B06 Transportation, logistics and supply chain management
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