Admissibility and entropy dissipation of distributional solution to Aw-Rascle traffic model

It is well known that classical theory of conservation laws system often fails, in the sense that classical smooth solution usually breaks down in finite time leading to formation of often unbounded (singular) solutions. In this paper we construct approximate solution to Aw-Rascle traffic model subjected to distributional initial data and discuss admissibility of obtained solution. The method is based on initial data approximation which brings the question about uniqueness of distributional limit. In order to single out proper solution we use the Backward entropy condition which states that admissible solution is the one that induces minimal dissipation of mathematical entropy to the system. The importance of these kind of problems lies in the fact that they can be interpreted as singular interaction problems appearing in the process of formation of approximate solution to general initial value problem.