Free Access
Issue
ESAIM: COCV
Volume 17, Number 2, April-June 2011
Page(s) 353 - 379
DOI https://doi.org/10.1051/cocv/2010007
Published online 24 March 2010
  1. C.E. Agnew, Dynamic modeling and control of congestion-prone systems. Oper. Res. 24 (1976) 400–419. [CrossRef]
  2. L. Ambrosio, Transport equation and Cauchy problem for non-smooth vector fields, in Calculus of variations and nonlinear partial differential equations, Lecture Notes in Math. 1927, Springer, Berlin, Germany (2008) 1–41.
  3. D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains. SIAM J. Appl. Math. 66 (2006) 896–920. [CrossRef] [MathSciNet]
  4. D. Armbruster, D.E. Marthaler, C. Ringhofer, K. Kempf and T.-C. Jo, A continuum model for a re-entrant factory. Oper. Res. 54 (2006) 933–950. [CrossRef]
  5. S. Benzoni-Gavage, R.M. Colombo and P. Gwiazda, Measure valued solutions to conservation laws motivated by traffic modelling. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006) 1791–1803. [CrossRef] [MathSciNet]
  6. S. Bianchini, On the shift differentiability of the flow generated by a hyperbolic system of conservation laws. Discrete Contin. Dynam. Systems 6 (2000) 329–350. [CrossRef] [MathSciNet]
  7. F. Bouchut and F. James, One-dimensional transport equations with discontinuous coefficients. Nonlinear Anal. 32 (1998) 891–933. [CrossRef] [MathSciNet]
  8. F. Bouchut and F. James, Differentiability with respect to initial data for a scalar conservation law, in Hyperbolic problems: theory, numerics, applications, Internat. Ser. Numer. Math., Birkhäuser, Basel, Switzerland (1999).
  9. A. Bressan and G. Guerra, Shift-differentiability of the flow generated by a conservation law. Discrete Contin. Dynam. Systems 3 (1997) 35–58. [MathSciNet]
  10. A. Bressan and M. Lewicka, Shift differentials of maps in BV spaces, in Nonlinear theory of generalized functions (Vienna, 1997), Res. Notes Math. 401, Chapman & Hall/CRC, Boca Raton, USA (1999) 47–61.
  11. A. Bressan and W. Shen, Optimality conditions for solutions to hyperbolic balance laws, in Control methods in PDE-dynamical systems, Contemp. Math. 426, AMS, USA (2007) 129–152.
  12. C. Canuto, F. Fagnani and P. Tilli, A eulerian approach to the analysis of rendez-vous algorithms, in Proceedings of the IFAC World Congress (2008).
  13. R.M. Colombo and A. Groli, On the optimization of the initial boundary value problem for a conservation law. J. Math. Analysis Appl. 291 (2004) 82–99. [CrossRef]
  14. R.M. Colombo and M.D. Rosini, Pedestrian flows and non-classical shocks. Math. Methods Appl. Sci. 28 (2005) 1553–1567. [CrossRef] [MathSciNet]
  15. R.M. Colombo, M. Mercier and M.D. Rosini, Stability and total variation estimates on general scalar balance laws. Commun. Math. Sci. 7 (2009) 37–65. [MathSciNet]
  16. R.M. Colombo, G. Facchi, G. Maternini and M.D. Rosini, On the continuum modeling of crowds, in Hyperbolic Problems: Theory, Numerics, Applications 67, Proceedings of Symposia in Applied Mathematics, E. Tadmor, J.-G. Liu and A.E. Tzavaras Eds., American Mathematical Society, Providence, USA (2009).
  17. V. Coscia and C. Canavesio, First-order macroscopic modelling of human crowd dynamics. Math. Models Methods Appl. Sci. 18 (2008) 1217–1247. [CrossRef] [MathSciNet]
  18. M. Gugat, M. Herty, A. Klar and G. Leugering, Conservation law constrained optimization based upon Front-Tracking. ESAIM: M2AN 40 (2006) 939–960. [CrossRef] [EDP Sciences]
  19. R.L. Hughes, A continuum theory for the flow of pedestrians. Transportation Res. Part B 36 (2002) 507–535. [CrossRef]
  20. U. Karmarkar, Capacity loading and release planning in work-in-progess (wip) and lead-times. J. Mfg. Oper. Mgt. 2 (1989) 105–123.
  21. S.N. Kružkov, First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (1970) 228–255. [MathSciNet]
  22. M. Marca, D. Armbruster, M. Herty and C. Ringhofer, Control of continuum models of production systems. IEEE Trans. Automat. Contr. (to appear).
  23. B. Perthame and A.-L. Dalibard, Existence of solutions of the hyperbolic Keller-Segel model. Trans. Amer. Math. Soc. 361 (2009) 2319–2335. [CrossRef] [MathSciNet]
  24. S. Ulbrich, A sensitivity and adjoint calculus for discontinuous solutions of hyperbolic conservation laws with source terms. SIAM J. Control Optim. 41 (2002) 740. [CrossRef] [MathSciNet]
  25. S. Ulbrich, Adjoint-based derivative computations for the optimal control of discontinuous solutions of hyperbolic conservation laws. Syst. Contr. Lett. 48 (2003) 313–328. [CrossRef]
  26. V.I. Yudovič, Non-stationary flows of an ideal incompressible fluid. Ž. Vyčisl. Mat. i Mat. Fiz. 3 (1963) 1032–1066.

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