LJK-Deterministic Models and Algorithms: EDP-AIRSEA-CVGI Seminar
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On Thursday February 14 2019 at 11h00 in Room 106 - IMAG Building
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Seminary of Mr Nicolas LAURENT-BROUTY (Inria Sophia Antipolis)
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The zero relaxation limit for the Aw-Rascle-Zhang traffic flow model
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Summary
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In this talk we will detail the mathematical behavior of the Aw-Rascle-Zhang 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 Wave-Front-Tracking 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 Aw-Rascle-Zhang system with relaxation converge to a weak solution of the corresponding scalar conservation law when the relaxation parameter goes to zero.
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