Free Access
Volume 19, Number 1, January-March 2013
Page(s) 129 - 166
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).
  2. Y. Achdou, F. Camilli, A. Cutri and N. Tchou, Hamilton-Jacobi equations on networks, in 18th IFAC World Congress. Milano, Italy (2011).
  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. [CrossRef] [MathSciNet]
  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.
  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. [CrossRef] [MathSciNet]
  6. G. Barles, Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations : a guided visit. Nonlinear Anal. 20 (1993) 1123–1134. [CrossRef] [MathSciNet]
  7. G. Barles, Solutions de viscosité des équations de Hamilton-Jacobi, Mathématiques & Applications (Berlin) [Mathematics & Applications] 17, Springer-Verlag, Paris (1994).
  8. A. Bressan and Y. Hong, Optimal control problems on stratified domains. Netw. Heterog. Media 2 (2007) 313–331 (electronic). [CrossRef] [MathSciNet]
  9. A. Briani and A. Davini, Monge solutions for discontinuous Hamiltonians. ESAIM : COCV 11 (2005) 229–251 (electronic). [CrossRef] [EDP Sciences]
  10. R. Bürger and K.H. Karlsen, Conservation laws with discontinuous flux : a short introduction. J. Engrg. Math. 60 (2008) 241–247. [CrossRef] [MathSciNet]
  11. F. Camilli and D. Schieborn, Viscosity solutions of eikonal equations on topological networks. Preprint.
  12. X. Chen and B. Hu, Viscosity solutions of discontinuous Hamilton-Jacobi equations. Interfaces and Free Boundaries 10 (2008) 339–359. [CrossRef] [MathSciNet]
  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]
  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. [CrossRef] [EDP Sciences]
  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]
  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]
  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.
  18. M. Garavello and B. Piccoli, Conservation laws on complex networks. Ann. Inst. Henri. Poincaré, Anal. Non Linéaire 26 (2009) 1925–1951. [CrossRef]
  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. [CrossRef] [MathSciNet]
  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]
  21. M. Garavello, R. Natalini, B. Piccoli, and A. Terracina, Conservation laws with discontinuous flux. Netw. Heterog. Media 2 (2007) 159–179. [CrossRef] [MathSciNet]
  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.
  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.
  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.
  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. [CrossRef] [MathSciNet]
  26. P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Math. 69. Pitman Advanced Publishing Program, Mass Boston (1982).
  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]
  28. R.T. Newcomb II and J. Su, Eikonal equations with discontinuities. Differential Integral Equations 8 (1995) 1947–1960. [MathSciNet]
  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. [CrossRef] [MathSciNet]
  30. P.I. Richards, Shock waves on the highway. Operation Research 4 (1956) 42–51. [CrossRef] [MathSciNet]
  31. D. Schieborn, Viscosity Solutions of Hamilton-Jacobi Equations of Eikonal Type on Ramified Spaces. Ph.D. thesis, Eberhard-Karls-Universitat Tubingen (2006).
  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]
  33. A. Siconolfi, Metric character of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 355 (2003) 1987–2009 (electronic). [CrossRef]
  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]
  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]
  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]
  37. P. Soravia, Boundary value problems for Hamilton-Jacobi equations with discontinuous Lagrangian. Indiana Univ. Math. J. 51 (2002) 451–477. [MathSciNet]
  38. P. Soravia, Uniqueness results for fully nonlinear degenerate elliptic equations with discontinuous coefficients. Commun. Pure Appl. Anal. 5 (2006) 213–240. [CrossRef] [MathSciNet]
  39. T. Strömberg, On viscosity solutions of irregular Hamilton-Jacobi equations. Arch. Math. (Basel) 81 (2003) 678–688. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.