Convergence of a misanthrope process to the entropy solution of 1D problems |
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Authors: | R. Eymard M. Roussignol A. Tordeux |
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Affiliation: | 1. Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, Cité Descartes - Champs-sur-Marne - F-77454 Marne-la-Vallée, Cedex 2, France;2. Laboratoire Ville Mobilité Transport, Université Paris-Est, Cité Descartes - Champs-sur-Marne - F-77454 Marne-la-Vallée, Cedex 2, France |
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Abstract: | We prove the convergence, in some strong sense, of a Markov process called “a misanthrope process” to the entropy weak solution of a one-dimensional scalar nonlinear hyperbolic equation. Such a process may be used for the simulation of traffic flows. The convergence proof relies on the uniqueness of entropy Young measure solutions to the nonlinear hyperbolic equation, which holds for both the bounded and the unbounded cases. In the unbounded case, we also prove an error estimate. Finally, numerical results show how this convergence result may be understood in practical cases. |
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Keywords: | Misanthrope stochastic process Non linear scalar hyperbolic equation Entropy Young measure solution Traffic flow simulation Weak BV inequality |
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