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References:
[1] |
D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, NoDEA Nonlinear Differential Equations and Applications, 4 (1997), 1-42.
doi: 10.1007/PL00001406. |
[2] |
C. Bardos, A. Leroux and J. Nedelec, First order quasilinear equations with boundary conditions, Commun. Partial Diff. Equat., 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
[3] |
A. Bressan, "Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem," Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford, 2000. |
[4] |
M. G. Crandall, L. C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. AMS., 282 (1984), 487-502.
doi: 10.1090/S0002-9947-1984-0732102-X. |
[5] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. |
[6] |
H. Frankowska, On LeFloch solutions to initial-boundary value problem for scalar conservation laws, Journal of Hyperbolic Differential Equations, 7 (2010), 503-543.
doi: 10.1142/S0219891610002219. |
[7] |
H. Frankowska, Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations, Proceedings of 30th CDC Conference, IEEE, Brighton, December 11-13, (1991), 265-270. |
[8] |
H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equation, SIAM J. Control and Optimization, 31 (1993), 257-272.
doi: 10.1137/0331016. |
[9] |
P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[10] |
P. G. LeFloch, Explicit formula for scalar nonlinear conservation laws with boundary condition, Math. Methods Appl. Sci., 10 (1988), 265-287.
doi: 10.1002/mma.1670100305. |
[11] |
M. Lighthill and G. Whitham, On kinematic waves, II: A theory of traffic flow on long crowded roads, Proceedings of the Royal Society of London Ser. A., 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[12] |
P. Richards, Shock waves on the highway, Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[13] |
I. Strub and A. Bayen, Weak formulation of boundary conditions for scalar conservation laws: An application to highway traffic modelling, Int. J. Robust Nonlinear Control, 16 (2006), 733-748.
doi: 10.1002/rnc.1099. |
show all references
References:
[1] |
D. Amadori, Initial-boundary value problems for nonlinear systems of conservation laws, NoDEA Nonlinear Differential Equations and Applications, 4 (1997), 1-42.
doi: 10.1007/PL00001406. |
[2] |
C. Bardos, A. Leroux and J. Nedelec, First order quasilinear equations with boundary conditions, Commun. Partial Diff. Equat., 4 (1979), 1017-1034.
doi: 10.1080/03605307908820117. |
[3] |
A. Bressan, "Hyperbolic Systems of Conservation Laws: The One-dimensional Cauchy Problem," Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford, 2000. |
[4] |
M. G. Crandall, L. C. Evans and P.-L. Lions, Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. AMS., 282 (1984), 487-502.
doi: 10.1090/S0002-9947-1984-0732102-X. |
[5] |
L. C. Evans, "Partial Differential Equations," Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 1998. |
[6] |
H. Frankowska, On LeFloch solutions to initial-boundary value problem for scalar conservation laws, Journal of Hyperbolic Differential Equations, 7 (2010), 503-543.
doi: 10.1142/S0219891610002219. |
[7] |
H. Frankowska, Lower semicontinuous solutions to Hamilton-Jacobi-Bellman equations, Proceedings of 30th CDC Conference, IEEE, Brighton, December 11-13, (1991), 265-270. |
[8] |
H. Frankowska, Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equation, SIAM J. Control and Optimization, 31 (1993), 257-272.
doi: 10.1137/0331016. |
[9] |
P. D. Lax, Hyperbolic systems of conservation laws II, Comm. Pure Appl. Math., 10 (1957), 537-566.
doi: 10.1002/cpa.3160100406. |
[10] |
P. G. LeFloch, Explicit formula for scalar nonlinear conservation laws with boundary condition, Math. Methods Appl. Sci., 10 (1988), 265-287.
doi: 10.1002/mma.1670100305. |
[11] |
M. Lighthill and G. Whitham, On kinematic waves, II: A theory of traffic flow on long crowded roads, Proceedings of the Royal Society of London Ser. A., 229 (1955), 317-345.
doi: 10.1098/rspa.1955.0089. |
[12] |
P. Richards, Shock waves on the highway, Operations Research, 4 (1956), 42-51.
doi: 10.1287/opre.4.1.42. |
[13] |
I. Strub and A. Bayen, Weak formulation of boundary conditions for scalar conservation laws: An application to highway traffic modelling, Int. J. Robust Nonlinear Control, 16 (2006), 733-748.
doi: 10.1002/rnc.1099. |
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