References
- J. Aleksić, D. Mitrovic and S. Pilipović. Hyperbolic conservation laws with vanishing nonlinear diffusion and linear dispersion in heterogeneous media. Journal of Evolution Equations, 9(4):809–828, 2009. http://dx.doi.org/10.1007/s00028-009-0035-5.
- K. Ammar, P. Wittbold and J. Carrillo. Scalar conservation laws with general boundary condition and continuous flux function. Journal of Differential Equations, 228(1):111–139, 2006. http://dx.doi.org/10.1016/j.jde.2006.05.002.
- B. Andreianov and D. Mitrovíc. Entropy conditions for scalar conservation laws with discontinuous flux revisited. Annales de l’Institut Henri Poincare (C) Non Linear Analysis, 32(6):1307–1335, 2015. http://dx.doi.org/10.1016/j.anihpc.2014.08.002.
- B. Andreianov and K. Sbihi. Well-posedness of general boundary-value problems for scalar conservation laws. Transactions of the American Mathematical Society, 367:3763–3806, 2015. http://dx.doi.org/10.1090/S0002-9947-2015-05988-1#sthash.4STac3SY.dpuf.
- C. Bardos, A.Y. Leroux and J.C. Nedelec. First order quasilinear equations with boundary conditions. Communications in Partial Differential Equations, 4(9):1017–1034, 1979. http://dx.doi.org/10.1080/03605307908820117.
- R. Borsche, R.M. Colombo and M. Garavello. Mixed systems: ODEsbalance laws. Journal of Differential Equations, 252(3):2311–2338, 2012. http://dx.doi.org/10.1016/j.jde.2011.08.051.
- R. Bürger, H. Frid and K.H. Karlsen. On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition. Journal of Mathematical Analysis and Applications, 326(1):108–120, 2007. http://dx.doi.org/10.1016/j.jmaa.2006.02.072.
- R. Bürger and W. L. Wendland. Entropy boundary and jump conditions in the theory of sedimentation with compression. Mathematical Methods in the Applied Sciences, 21(9):865–882, 1998. doi: 10.1002/(SICI)1099-1476(199806)21:9<865::AID-MMA983>3.0.CO;2-9
- G. M. Coclite and M. Garavello. Vanishing viscosity for mixed systems with moving boundaries. Journal of Functional Analysis, 264(7):1664–1710, 2013. http://dx.doi.org/10.1016/j.jfa.2013.01.010.
- G.M. Coclite, M. Garavello and B. Piccoli. Traffic flow on a road network. SIAM Journal on Mathematical Analysis, 36(6):1862–1886, 2005. http://dx.doi.org/10.1137/S0036141004402683.
- G.M. Coclite, K.H. Karlsen and Y.-S. Kwon. Initial-boundary value problems for conservation laws with source terms and the DegasperisProcesi equation. Journal of Functional Analysis, 257(12):3823–3857, 2009. http://dx.doi.org/10.1016/j.jfa.2009.09.022.
- R.J. DiPerna. Convergence of the viscosity method for isentropic gas dynamics. Communications in Mathematical Physics, 91(1):1–30, 1983. http://dx.doi.org/10.1007/BF01206047.
- L.C. Evans. Weak Convergence Methods for Nonlinear Partial Differential Equations. American Mathematical Society, 1990. CBMS Regional Conference Series in Mathematics. Volume 74
- H. Greenberg. An analysis of traffic flow. Operations Research, 7(1):79–85, 1959. http://dx.doi.org/10.1287/opre.7.1.79.
- C. Imbert and J. Vovelle. A kinetic formulation for multidimensional scalar conservation laws with boundary conditions and applications. SIAM Journal on Mathematical Analysis, 36(1):214–232, 2004. http://dx.doi.org/10.1137/S003614100342468X.
- C.I. Kondo and P.G. LeFloch. Zero diffusion-dispersion limits for scalar conservation laws. SIAM Journal on Mathematical Analysis, 33(6):1320–1329, 2002. http://dx.doi.org/10.1137/S0036141000374269.
- Y.-S. Kwon and A. Vasseur. Strong traces for solutions to scalar conservation laws with general flux. Archive for Rational Mechanics and Analysis, 185(3):495–513, 2007. http://dx.doi.org/10.1007/s00205-007-0055-7.
- M.J. Lighthill and G.B. Whitham. On kinematic waves. ii. a theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 229(1178):317–345, 1955. http://dx.doi.org/10.1098/rspa.1955.0089.
- Y. Lu. Hyperbolic Conservation Laws and the Compensated Compactness Method. Chapman and Hall/CRC, 2002.
- E. Panov. On weak completeness of the set of entropy solutions to a scalar conservation law. SIAM Journal on Mathematical Analysis, 41(1):26–36, 2009. http://dx.doi.org/10.1137/080724587.
- E.Yu. Panov. On the Dirichlet problem for first order quasilinear equations on a manifold. Transactions of the American Mathematical Society, 363:2393–2446, 2011. http://dx.doi.org/10.1090/S0002-9947-2010-05016-0.
- H. J. Payne. Models of freeway traffic and control. In Frank C. Rieman(Ed.), Math. Models of Public Systems, Simulations Council Proceedings, pp. 51–60. Simulation Councils, Incorporated, 1971.
- P.I. Richards. Shock waves on the highway. Operations Research, 4(1):42–51, 1956. http://dx.doi.org/10.1287/opre.4.1.42.
- M.E. Schonbek. Convergence of solutions to nonlinear dispersive equations. Communications in Partial Differential Equations, 7(8):959–1000, 1982. http://dx.doi.org/10.1080/03605308208820242.
- I.S. Strub and A.M. Bayen. Mixed initial-boundary value problems for scalar conservation laws: Application to the modeling of transportation networks. In J.P. Hespanha and A. Tiwari(Eds.), Hybrid Systems: Computation and Control, volume 3927 of Lecture Notes in Computer Science, pp. 552–567, Berlin, Heidelberg, 2006. Springer Berlin Heidelberg. http://dx.doi.org/10.1007/1173063741.
- M. Svärd and S. Mishra. Entropy stable schemes for initial-boundary-value conservation laws. Zeitschrift für angewandte Mathematik und Physik, 63(6):985–1003, 2012. http://dx.doi.org/10.1007/s00033-012-0216-x.
- L. Tartar. Compensated compactness and applications to partial differential equations. In Nonlinear Analysis and Mechanics: Heriot-Watt Symposium, Vol. IV, Research Notes in Mathematics 39, pp. 136–212. Pitman, Boston, MassLondon, 1979.