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International Press, Communications in Mathematical Sciences, 3(1), p. 409-421

DOI: 10.4310/cms.2003.v1.n3.a2

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Entropy methods for kinetic models of traffic flow

Journal article published in 2003 by Jean Dolbeault ORCID, Reinhard Illner
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

In these notes we first introduce logarithmic entropy methods for time-dependent drift-diffusion equations and then consider a kinetic model of Vlasov-Fokker-Planck type for traffic flows. In the spatially homogeneous case the model reduces to a special type of nonlinear driftdiffusion equation which may permit the existence of several stationary states corresponding to the same density. Then we define general convex entropies and prove a convergence result for large times to steady states, even if more than one exists in the considered range of parameters, provided that some entropy estimates are uniformly bounded.