Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation

[EN] The phenomenon of chaos has been exhibited in mathematical nonlinear models that describe traffic flows, see, for instance (Li and Gao in Modern Phys Lett B 18(26-27):1395-1402, 2004; Li in Phys. D Nonlinear Phenom 207(1-2):41-51, 2005). At microscopic level, Devaney chaos and distributional chaos have been exhibited for some car-following models, such as the quick-thinking-driver model and the forward and backward control model (Barrachina et al. in 2015; Conejero et al. in Semigroup Forum, 2015). We present here the existence of chaos for the macroscopic model given by the Lighthill Whitham Richards equation.The authors are supported by MEC Project MTM2013-47093-P. The second and third authors are supported by GVA, Project PROMETEOII/2013/013Conejero, JA.; Martínez Jiménez, F.; Peris Manguillot, A.; Ródenas Escribá, FDA. (2016). Chaotic asymptotic behaviour of the solutions of the Lighthill Whitham Richards equation. 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