Resurrection of “second order” models of traffic flow
SIAM Journal on Applied Mathematics
Kinetic derivation of macroscopic anticipation models for vehicular traffic
SIAM Journal on Applied Mathematics
From the modelling of driver's behavior to hydrodynamic models and problems of traffic flow
Nonlinear Analysis: Real World Applications
An improved macroscopic model of traffic flow: Derivation and links with the Lighthill-Whitham model
Mathematical and Computer Modelling: An International Journal
Optimization of traffic flow conditions by minimization of quadratic functionals
Mathematical and Computer Modelling: An International Journal
A 2 × 2 hyperbolic traffic flow model
Mathematical and Computer Modelling: An International Journal
From experiments to hydrodynamic traffic flow models: I-modelling and parameter identification
Mathematical and Computer Modelling: An International Journal
Nonlinear hydrodynamic models of traffic flow modelling and mathematical problems
Mathematical and Computer Modelling: An International Journal
Hydrodynamic models of traffic flow: Drivers' behaviour and nonlinear diffusion
Mathematical and Computer Modelling: An International Journal
From experiments to hydrodynamic traffic flow models II-Sensitivity analysis
Mathematical and Computer Modelling: An International Journal
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This paper deals with the modeling and qualitative analysis, with special attention to hyperbolicity analysis, of a large class of second-order hydrodynamic traffic flow models. These models are obtained from conservation equations for mass and momentum properly closed by constitutive relations related to the modeling of the behaviour of drivers in the flow. The first part of the paper deals with defining the general mathematical setting for modeling second-order hydrodynamic equations of traffic flow related to conservation of mass and momentum, and the second part with analyzing the qualitative properties of some specific models. In particular, it is shown how some models known in the literature can be obtained as particular cases of the above framework. Finally, the third part develops a hyperbolicity analysis which is also referred to some specific models.