Entropy methods for kinetic models of traffic flow
Dolbeault, Jean ; Illner, Reinhard
Commun. Math. Sci., Tome 1 (2003) no. 1, p. 409-421 / Harvested from Project Euclid
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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.
Publié le : 2003-09-15
Classification:  Traffic flow,  time-dependent diffusions,  drift-diffusion equations,  nonlinear friction and diffusion coefficients,  entropy method,  relative entropy,  large time asymptotics,  90B20,  35K55,  35B40,  35B45,  94A17,  70F40,  60J60,  60J70,  92D99 
@article{1250880093,
     author = {Dolbeault, Jean and Illner, Reinhard},
     title = {Entropy methods for kinetic models of traffic flow},
     journal = {Commun. Math. Sci.},
     volume = {1},
     number = {1},
     year = {2003},
     pages = { 409-421},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1250880093}
}

Dolbeault, Jean; Illner, Reinhard. Entropy methods for kinetic models of traffic flow. Commun. Math. Sci., Tome 1 (2003) no. 1, pp.  409-421. http://gdmltest.u-ga.fr/item/1250880093/