Fluid Mathematical Models of Traffic Flow

I will start with a few basic facts on other types of description (microscopic, kinetic ...) Then I will talk about fluid models, of 'first order': Lighthill-Whitham-Richards (LWR) , i.e. a scalar conservation law, robust and (too ?) simple. The first type of "second order models" (Payne-Whitham) was based on the gas dynamics system and had severe drawbacks, like predicting sometimes cars moving backwards (!). After the classical paper of Daganzo ('Requiem ...', 95), we introduced with Aw ('Resurrection ...', 2000) a very simple fixing of this PW model, which definitely cures these inconsistencies. I will show the (rigorous) relations between this class of models and the microscopic 'Follow the Leader' models. Finally, if time allows, I will describe some apllications to flows on a network, and related issues, like homgenization problems, or hybrid schemes.