Center for Interdisciplinary Mathematics

Department of Mathematics

On Traffic Flow

  1. A. Bressan and K. Han, Optima and equilibria for a model of traffic flow. SIAM J. Math. Anal. 43 (2011), 2384–2417.
  2. A. Bressan and K. Han, Nash equilibria for a model of traffic flow with several groups of drivers, ESAIM; Control, Optim. Calc. Var., 18 (2012), 969–986.
  3. A. Bressan, C. J. Liu, W. Shen, and F. Yu, Variational analysis of Nash equilibria for a model of traffic flow, Quarterly Appl. Math. 70 (2012), 495–515.
  4. A. Bressan and K. Han, Existence of optima and equilibria for traffic flow on networks,Networks & Heter. Media, 8 (2013), 627–648.
  5. A.Bressan, S. Canic, M. Garavello, M. Herty, and B. Piccoli, Flow on networks: recent results and perspectives, EMS Surv. Math. Sci. 1 (2014), 47–111.
  6. A. Bressan and F. Yu, Continuous Riemann solvers for traffic flow at a junction. Discr. Cont. Dyn. Syst., 35 (2015), 4149–4171.
  7. A. Bressan and K. Nguyen, Conservation law models for traffic flow on a network of roads. Netw. Heter. Media, 10 (2015), 255–293 .
  8. A. Bressan and K.Nguyen, Optima and equilibria for traffic flow on networks with backward propagating queues, Netw. Heter. Media 10 (2015), 717–748.
  9. Alberto Bressan, Conservation law models on a network of roads, in: Theory, Numerics and Applications of Hyperbolic Problems I, pp. 237–248. C.Klingenberg and M.Westdickenberg Eds., Springer-Verlag, 2018.
  10. A.Bressan and A.Nordli, The Riemann Solver for traffic flow at an intersection with buffer of vanishing size. Netw. Heter. Media, 12 (2017), 173-189.
  11.  W. Shen and K. Shikh-Khalil. Traveling Waves for a Microscopic Model of Traffic Flow. Discrete and Continuous Dynamical Systems 38 (2018), 2571-2589.
  12. W.Shen. Traveling Wave Profiles for a Follow-the-Leader Model for Traffic Flow with Rough Road Condition.  Netw. Heterog. Media 13 (2018), 449-478.
  13.  J.Ridder and W.Shen. Traveling Waves for Nonlocal Models of Traffic Flow, Discrete and Continuous Dynamical Systems 39 (2019), 4001–4040.
  14. A.Bressan and Y.Huang, Globally optimal departure rates for several groups of drivers, Mathematics in Engineering 1 (2019), 583–613.
  15. A.Bressan and W.Shen. On traffic flow with nonlocal flux: a relaxation representation, Archive Rational Mech. Anal. 237 (2020), 1213–1236.
  16. A.Bressan and W.Shen. Entropy admissibility of the limit solution
    for a nonlocal model of traffic flow, Comm. Math. Sci. 19 (2021), 1447–1450.