ENTROPY METHODS FOR KINETIC MODELS OF TRAFFIC FLOW

Communications in Mathematical Sciences

Volumn 1, Issue 3, 2003, Pages 409-421

  Dolbeault, Jean ^a   Illner, Reinhard ^b  

^a UNIVERSITÉ PARIS DESCARTES   (France)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Drift diffusion equations; Entropy method; Large time asymptotics; Nonlinear friction and diffusion coefficients; Relative entropy; Time dependent diffusions; Traffic flow

Indexed keywords

EID: 33845756523     PISSN: 15396746     EISSN: 19450796     Source Type: Journal    
DOI: 10.4310/CMS.2003.v1.n3.a2     Document Type: Article

References (7)

1. [1] A. Arnold, P. Markowich, G. Toscani, and A. Unterreiter, On convex Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations, Comm. P.D.E., 26:43-100, 2001.
2. [2] J.A. Carrillo, A. Jüngel, P.A. Markowich, G. Toscani, and A. Unterreiter, Entropy dissipation methods for degenerate parabolic problems and generalized sobolev inequalities, Monatsh. Math., 133:1-82, 2001.
3. [3] J. Dolbeault, R. Illner, and M. Kowalczyk, Entropy methods for explicitely time-dependent drift-diffusion equations, in preparation.
4. [4] R. Illner, A. Klar, and Th. Materne, Vlasov-Fokker-Planck models for multilane traffic flow, Comm. Math. Sci., 1(1):1-12, 2003.
5. [5] R. Illner, A. Klar, and Th. Materne, On Vlasov-Fokker-Planck type kinetic models for multilane traffic flow, to appear in Proceedings of the 23rd International Symposium on Rarefied Gas Dynamics,. Eds., Ph. Muntz and A. Ketsdever, 2003.
6. [6] R. Illner, C. Stoica, A. Klar, and R. Wegener, Kinetic equilibria in traffic flow models, Transport Theory Stat. Phys., 31(7):615-634, 2002.
7. [7] F. Otto, The geometry of dissipative evolution equations: the porous medium equation, Comm.P.D.E., 26(1-2):101-174, 2001.