On entropy conditions and traffic flow models

Abstract

This paper is concerned with "entropy conditions" for traffic flow models governed by one-dimensional nonlinear scalar conservation laws. The classical conditions of this type serve as selection principles used to overcome the lack of uniqueness of weak solutions for such laws. These principles select solutions in accord with observations for the simplest traffic flow models, but they seem not to do so when the constitutive law underlying the model is refined so as to be more realistic. The classical conditions are here compared with an analog of the second law of thermodynamics based on an entropy density that crudely measures the disorder of the traffic flow.

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