Free Access
Volume 18, Number 4, October-December 2012
Page(s) 969 - 986
Published online 16 January 2012
  1. J.P. Aubin and A. Cellina, Differential inclusions. Set-Valued Maps and Viability Theory. Springer-Verlag, Berlin (1984). [Google Scholar]
  2. A. Bressan and K. Han, Optima and equilibria for a model of traffic flow. SIAM J. Math. Anal. 43 (2011) 2384–2417. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Cellina, Approximation of set valued functions and fixed point theorems. Ann. Mat. Pura Appl. 82 (1969) 17–24. [CrossRef] [MathSciNet] [Google Scholar]
  4. F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York (1998). [Google Scholar]
  5. T.L. Friesz, Dynamic Optimization and Differential Games, Springer, New York (2010). [Google Scholar]
  6. T.L. Friesz, T. Kim, C. Kwon and M.A. Rigdon, Approximate network loading and dual-time-scale dynamic user equilibrium. Transp. Res. Part B (2010). [Google Scholar]
  7. A. Fügenschuh, M. Herty and A. Martin, Combinatorial and continuous models for the optimization of traffic flows on networks. SIAM J. Optim. 16 (2006) 1155–1176. [CrossRef] [Google Scholar]
  8. M. Garavello and B. Piccoli, Traffic Flow on Networks. Conservation Laws Models. AIMS Series on Applied Mathematics, Springfield, Mo. (2006). [Google Scholar]
  9. M. Gugat, M. Herty, A. Klar and G. Leugering, Optimal control for traffic flow networks. J. Optim. Theory Appl. 126 (2005) 589–616. [CrossRef] [MathSciNet] [Google Scholar]
  10. M. Herty, C. Kirchner and A. Klar, Instantaneous control for traffic flow. Math. Methods Appl. Sci. 30 (2007) 153–169. [CrossRef] [Google Scholar]
  11. L.C. Evans, Partial Differential Equations, 2nd edition. American Mathematical Society, Providence, RI (2010). [Google Scholar]
  12. P.D. Lax, Hyperbolic systems of conservation laws II. Commun. Pure Appl. Math. 10 (1957) 537–566. [Google Scholar]
  13. M. Lighthill and G. Whitham, On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A 229 (1955) 317–345. [Google Scholar]
  14. P.I. Richards, Shock waves on the highway. Oper. Res. 4 (1956), 42–51. [Google Scholar]
  15. J. Smoller, Shock waves and reaction-diffusion equations, 2nd edition. Springer-Verlag, New York (1994). [Google Scholar]

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