LJKDeterministic Models and Algorithms: EDPAIRSEACVGI Seminar

On Thursday February 14 2019 at 11h00 in Room 106  IMAG Building

Seminary of Mr Nicolas LAURENTBROUTY (Inria Sophia Antipolis)

The zero relaxation limit for the AwRascleZhang traffic flow model

Summary

In this talk we will detail the mathematical behavior of the AwRascleZhang model with relaxation. This model, which consists in a 2x2 hyperbolic system of balance laws, can now be considered as a classical traffic flow model. In a Lagrangian setting, we use the WaveFrontTracking method with splitting technique to construct a sequence of approximate solutions. We prove that this sequence admits a limit. We then show that the limit is a weak entropy solution of the relaxed system associated to a given initial datum with bounded variation. Besides, we also provide an estimate on the decay of positive waves. We finally prove that the solutions of the AwRascleZhang system with relaxation converge to a weak solution of the corresponding scalar conservation law when the relaxation parameter goes to zero.
