Open Access
September 2003 Entropy methods for kinetic models of traffic flow
Jean Dolbeault, Reinhard Illner
Commun. Math. Sci. 1(3): 409-421 (September 2003).


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.


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Jean Dolbeault. Reinhard Illner. "Entropy methods for kinetic models of traffic flow." Commun. Math. Sci. 1 (3) 409 - 421, September 2003.


Published: September 2003
First available in Project Euclid: 21 August 2009

zbMATH: 1134.90336
MathSciNet: MR2069937

Primary: 35B40 , 35B45 , 35K55 , 60J60 , 60J70 , 70F40 , 90B20 , 92D99 , 94A17

Keywords: drift-diffusion equations , entropy method , large time asymptotics , nonlinear friction and diffusion coefficients , Relative entropy , time-dependent diffusions , traffic flow

Rights: Copyright © 2003 International Press of Boston

Vol.1 • No. 3 • September 2003
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