Free Access
Issue
ESAIM: COCV
Volume 19, Number 1, January-March 2013
Page(s) 129 - 166
DOI https://doi.org/10.1051/cocv/2012002
Published online 01 March 2012
  1. Y. Achdou, F. Camilli, A. Cutri and N. Tchou, Hamilton-Jacobi equations on networks. Tech. Rep., preprint HAL 00503910 (2010). [Google Scholar]
  2. Y. Achdou, F. Camilli, A. Cutri and N. Tchou, Hamilton-Jacobi equations on networks, in 18th IFAC World Congress. Milano, Italy (2011). [Google Scholar]
  3. F. Bachmann and J. Vovelle, Existence and uniqueness of entropy solution of scalar conservation laws with a flux function involving discontinuous coefficients. Comm. Partial Differential Equations 31 (2006) 371–395. [Google Scholar]
  4. M. Bardi and I. Capuzzo-Dolcetta, Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems & Control : Foundations & Applications, Birkhäuser Boston Inc., Boston, MA (1997). With appendices by Maurizio Falcone and Pierpaolo Soravia. [Google Scholar]
  5. C. Bardos, A.Y. le Roux and J.-C. Nédélec, First order quasilinear equations with boundary conditions. Comm. Partial Differential Equations 4 (1979) 1017–1034. [Google Scholar]
  6. G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations : a guided visit. Nonlinear Anal. 20 (1993) 1123–1134. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques & Applications (Berlin) [Mathematics & Applications] 17, Springer-Verlag, Paris (1994). [Google Scholar]
  8. A. Bressan and Y. Hong, Optimal control problems on stratified domains. Netw. Heterog. Media 2 (2007) 313–331 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Briani and A. Davini, Monge solutions for discontinuous Hamiltonians. ESAIM : COCV 11 (2005) 229–251 (electronic). [Google Scholar]
  10. R. Bürger and K.H. Karlsen, Conservation laws with discontinuous flux : a short introduction. J. Engrg. Math. 60 (2008) 241–247. [CrossRef] [MathSciNet] [Google Scholar]
  11. F. Camilli and D. Schieborn, Viscosity solutions of eikonal equations on topological networks. Preprint. [Google Scholar]
  12. X. Chen and B. Hu, Viscosity solutions of discontinuous Hamilton-Jacobi equations. Interfaces and Free Boundaries 10 (2008) 339–359. [CrossRef] [MathSciNet] [Google Scholar]
  13. G.M. Coclite and N.H. Risebro, Viscosity solutions of Hamilton-Jacobi equations with discontinuous coefficients. J. Hyperbolic Differ. Equ. 4 (2007) 771–795. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Dal Maso and H. Frankowska, Value function for Bolza problem with discontinuous Lagrangian and Hamilton-Jacobi inequalities. ESAIM : COCV 5 (2000) 369–394. [Google Scholar]
  15. K.-J. Engel, M. Kramar Fijavž, R. Nagel and E. Sikolya, Vertex control of flows in networks. Netw. Heterog. Media 3 (2008) 709–722. [CrossRef] [MathSciNet] [Google Scholar]
  16. A. Fathi, Théorème KAM faible et théorie de Mather sur les systèmes Lagrangiens. C. R. Acad. Sci. Paris, Sér. I Math. 324 (1997) 1043–1046. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Garavello and B. Piccoli, Traffic flow on networks, AIMS Series on Applied Mathematics 1. American Institute of Mathematical Sciences (AIMS), Springfield, MO (2006). Conservation laws models. [Google Scholar]
  18. M. Garavello and B. Piccoli, Conservation laws on complex networks. Ann. Inst. Henri. Poincaré, Anal. Non Linéaire 26 (2009) 1925–1951. [Google Scholar]
  19. M. Garavello and P. Soravia, Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost. Nonlinear Differential Equations Appl. 11 (2004) 271–298. [Google Scholar]
  20. M. Garavello and P. Soravia, Representation formulas for solutions of the HJI equations with discontinuous coefficients and existence of value in differential games. J. Optim. Theory Appl. 130 (2006) 209–229. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Garavello, R. Natalini, B. Piccoli, and A. Terracina, Conservation laws with discontinuous flux. Netw. Heterog. Media 2 (2007) 159–179. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.-P. Lebacque, The Godunov scheme and what it means for first order traffic flow models. Internaional Symposium on Transportation and Traffic Theory 13 (1996) 647–677. [Google Scholar]
  23. J.-P. Lebacque and M.M. Khoshyaran, Modelling vehicular traffic flow on networks using macroscopic models, in Finite volumes for complex applications II. Hermes Sci. Publ., Paris (1999) 551–558. [Google Scholar]
  24. J.-P. Lebacque and M.M. Khoshyaran, First order macroscopic traffic flow models : intersection modeling, network modeling, in Transportation and Traffic Theory, Flow, Dynamics and Human Interaction. Elsevier (2005) 365–386. [Google Scholar]
  25. M.J. Lighthill and G.B. Whitham, On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. A 229 (1955) 317–145. [Google Scholar]
  26. P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Math. 69. Pitman Advanced Publishing Program, Mass Boston (1982). [Google Scholar]
  27. P.-L. Lions and P.E. Souganidis, Differential games, optimal control and directional derivatives of viscosity solutions of Bellman’ and Isaacs’ equations. SIAM J. Control Optim. 23 (1985) 566–583. [CrossRef] [MathSciNet] [Google Scholar]
  28. R.T. Newcomb II and J. Su, Eikonal equations with discontinuities. Differential Integral Equations 8 (1995) 1947–1960. [MathSciNet] [Google Scholar]
  29. D.N. Ostrov, Solutions of Hamilton-Jacobi equations and scalar conservation laws with discontinuous space-time dependence. J. Differential Equations 182 (2002) 51–77. [Google Scholar]
  30. P.I. Richards, Shock waves on the highway. Operation Research 4 (1956) 42–51. [Google Scholar]
  31. D. Schieborn, Viscosity Solutions of Hamilton-Jacobi Equations of Eikonal Type on Ramified Spaces. Ph.D. thesis, Eberhard-Karls-Universitat Tubingen (2006). [Google Scholar]
  32. N. Seguin and J. Vovelle, Analysis and approximation of a scalar conservation law with a flux function with discontinuous coefficients. Math. Models Methods Appl. Sci. 13 (2003) 221–257. [CrossRef] [Google Scholar]
  33. A. Siconolfi, Metric character of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 355 (2003) 1987–2009 (electronic). [CrossRef] [Google Scholar]
  34. P. Soravia, Discontinuous viscosity solutions to Dirichlet problems for Hamilton-Jacobi equations with convex Hamiltonians. Comm. Partial Differential Equations 18 (1993) 1493–1514. [CrossRef] [MathSciNet] [Google Scholar]
  35. P. Soravia, Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. I. Equations of unbounded and degenerate control problems without uniqueness. Adv. Differential Equations 4 (1999) 275–296. [MathSciNet] [Google Scholar]
  36. P. Soravia, Optimality principles and representation formulas for viscosity solutions of Hamilton-Jacobi equations. II. Equations of control problems with state constraints. Differential Integral Equations 12 (1999) 275–293. [MathSciNet] [Google Scholar]
  37. P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian. Indiana Univ. Math. J. 51 (2002) 451–477. [MathSciNet] [Google Scholar]
  38. P. Soravia, Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Commun. Pure Appl. Anal. 5 (2006) 213–240. [CrossRef] [MathSciNet] [Google Scholar]
  39. T. Strömberg, On viscosity solutions of irregular Hamilton-Jacobi equations. Arch. Math. (Basel) 81 (2003) 678–688. [CrossRef] [MathSciNet] [Google Scholar]

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