@article{AIHPC_2000__17_2_169_0, author = {Serre, Denis}, title = {Relaxations semi-lin\'eaire et cin\'etique des syst\`emes de lois de conservation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {17}, year = {2000}, pages = {169-192}, mrnumber = {1753092}, zbl = {0963.35117}, language = {fr}, url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_2_169_0} }
Serre, Denis. Relaxations semi-linéaire et cinétique des systèmes de lois de conservation. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 169-192. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_2_169_0/
[1] A relaxation approximation to a moment hierarchy of conservation laws with kinetic formulation, Quaderno IAC 23 (1997).
, , ,[2] Zero relaxation and dissipation limits for hyperbolic conservation laws, Comm. Pure Appl. Math. 46 (1994) 787-830. | MR 1213992 | Zbl 0797.35113
, ,[3] Hyperbolic conservation laws with stiff relaxation terms and entropy, Comm. Pure Appl. Math. 45 (1993) 755-781. | MR 1280989 | Zbl 0797.35113
, , ,[4] Positively invariant regions of nonlinear diffusion equations, Indiana Univ. Math. J. 26 (1977) 373-392. | MR 430536 | Zbl 0368.35040
, , ,[5] Convergence of the relaxation approximation to a scalar nonlinear hyperbolic equation arising in chromatography, Z. Angew. Math. Phys. 47 (1996) 400-409. | MR 1394915 | Zbl 0866.35061
, ,[6] Convergence of approximate solutions to conservation laws, Arch. Rat. Mech. Anal. 82 (1983) 27-70. | MR 684413 | Zbl 0519.35054
,[7] Existence and uniqueness of solutions for some hyperbolic systems of conservation laws, Arch. Rat. Mech. Anal. 126 (1994) 79-101. | MR 1268050 | Zbl 0810.35058
,[8] Invariant regions for systems of conservation laws, Trans. Amer. Math. Soc. 289 (1985) 591-610. | MR 784005 | Zbl 0535.35056
,[9] A convex entropy for a hyperbolic system with relaxation, J. Differential Equations 127 (1996) 95-107. | MR 1387259 | Zbl 0853.35066
,[10] The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Comm. Pure Appl. Math. 48 (1995) 235-277. | MR 1322811 | Zbl 0826.65078
, ,[11] Stability and convergence of relaxation schemes towards systems of conservation laws, Soumis.
, ,[12] Hyperbolic conservation laws with relaxation, Comm. Math. Phys. 108 (1987) 153-175. | MR 872145 | Zbl 0633.35049
,[13] L'injection du cône positif de H-1 dans W-1,q est compacte pour tout q < 2, J. Math. Pures et Appl. 60 (1981) 309-322. | Zbl 0471.46020
,[14] Convergence to equilibrium for the relaxation approximation of conservation laws, Comm. Pure Appl. Math. 49 (1996) 795-823. | MR 1391756 | Zbl 0872.35064
,[15] Recent results on hyperbolic relaxation problems, in: Analysis of Systems of Conervation Laws, Aachen, 1997, Chapman & Hall/CRC Monogr. Surv. Pure Appl. Math., Vol. 99, Chapman & Hall/CRC, Boca Raton, FL, 1999, pp. 128-197. | Zbl 0940.35127
,[16] A discrete kinetic approximation of entropy solutions to multidimensional scalar conservation laws, J. Differential Equations 148 (2) (1998) 292-317. | MR 1643175 | Zbl 0911.35073
,[ 17] The instant-response limit in Whitham's nonlinear traffic-flow model: uniform well-posedness, Asymptotic Anal. 1 (1988) 263-282. | MR 972301 | Zbl 0685.35099
,[ 18] Systèmes de Lois de Conservation, Diderot, Paris, 1996.
,[19] Convergence with physical viscosity for nonlinear elasticity, Preprint éternel, Lyon, 1993.
, ,[20] Global existence and compactness in LP for the quasi-linear wave equation, Comm. Partial Differential Equations 19 (1994) 1829-1877. | MR 1301175 | Zbl 0855.35078
,[21] Compensated compactness and applications to partial differential equations, in: Knops R.J. (Ed.), Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, Research Notes in Math., Vol. 39, Pitman, Londres, 1979, pp. 136-192. | MR 584398 | Zbl 0437.35004
,[22] On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term, SIAM J. Math. Anal.28 (1997) 136- 161. | MR 1427731 | Zbl 0868.35073
, ,[23] Materials with internal variables and relaxation to conservation laws, Preprint, Madison, 1998. | MR 1718478
,[24] Linear and Non-Linear Waves, Wiley, New York, 1974. | Zbl 0373.76001
,