Michel Rascle

Title: Some remarks on second order models of traffic flow.


I will talk about the general class of models:

$\dt \rho + \dx (\rho v)= 0$, $\rho$ : density, $v$ : velocity,
$\dt w + v \dx w = 0$, $w$ : Lagrangian marker, $v = f(\rho, w)$.

[This class of models is in fact much nearer to first order models, and
to their Hamilton-Jacobi aspects than to "classical" second order models, based on the (incorrect) Payne-Whitham model]

I will first recall the links with microscopic models (Follow the Leader). Then I will make a brief allusion to some recent developments,  and finally I will make a few comments on various possibilities of getting oscillating solutions for this class of models, which is (too ?) stable.