Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs
Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) no. 3-4, p. 351-417
@article{AIHPC_1991__8_3-4_351_0,
     author = {Serre, Denis},
     title = {Oscillations non lin\'eaires des syst\`emes hyperboliques : m\'ethodes et r\'esultats qualitatifs},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {8},
     number = {3-4},
     year = {1991},
     pages = {351-417},
     zbl = {0810.35060},
     mrnumber = {1127931},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPC_1991__8_3-4_351_0}
}
Serre, Denis. Oscillations non linéaires des systèmes hyperboliques : méthodes et résultats qualitatifs. Annales de l'I.H.P. Analyse non linéaire, Tome 8 (1991) no. 3-4, pp. 351-417. http://www.numdam.org/item/AIHPC_1991__8_3-4_351_0/

[1] J.M. Ball, Constitutive Inequalities and Existence Theorems in Non-Linear Elastostatics. Nonlinear Analysis and Mechanics. Herriot-Watt Symposium, Edinburgh, vol. I, 1976, p. 187-241, KNOPS éd., Pitman. | MR 478899 | Zbl 0377.73043

[2] M. Bonnefille, Thèse, Saint-Étienne, France, 1987.

[3] M. Bonnefille, Propagation des oscillations dans deux classes de systèmes hyperboliques (2 × 2 et 3 × 3), Comm. in PDEs, vol. 13, 1988, p. 905-925. | MR 944435 | Zbl 0649.35058

[4] K.N. Chueh, C.C. Conley et J.A. Smoller, Positively Invariant Regions for Systems of Nonlinear Diffusion Equations, Indiana Univ. Math. J., vol. 26, 1977, p. 373-392. | MR 430536 | Zbl 0368.35040

[5] B.D. Coleman et E.H. Dill, Z. Angew. Math. Phys., vol. 22, 1971, p. 691-702. | Zbl 0218.35072

[6] C. Dafermos, Estimates for Conservation Laws with Little Viscosity, S.I.A.M. J. Math. Anal., vol. 18, 1987. | MR 876280 | Zbl 0655.35055

[7] R.J. Diperna, Uniqueness of Solutions to Hyperbolic Systems of Conservation Laws, Indiana Univ. Math. J., vol. 28, 1979, p. 137-188. | MR 523630 | Zbl 0409.35057

[8] R.J. Diperna, Convergence of Approximate Solutions to Conservation Laws, Arch Rat. Mech. Anal., vol. 82, 1983, p. 27-70. | MR 684413 | Zbl 0519.35054

[9] R.J. Diperna, Measured-Valued Solutions to Conservation Laws, Arch. Rat. Mech. Anal., vol. 88, 1985, p. 223-270. | MR 775191 | Zbl 0616.35055

[10] H.G. Gilquin, Glimm's Scheme and Conservation Laws of Mixed Type, S.I.A.M. J. Sci. Stat. Comput., vol. 10, 1989, p. 133-153. | MR 976167 | Zbl 0668.73017

[11] H.G. Gilquin et D. Serre, Well-Posedness of the Riemann Problem; Consistency of the Godunov's Scheme. Proceeding of an A.M.S.-S.I.A.M. conference, Bowdoin college, 1988, GLIMM, KEYFITZ et LINDQUIST éd., Contemporary Mathematics n° 100.AMS, Providence, 1989. | Zbl 0685.65085

[12] J. Glimm, Solutions in the Large for Nonlinear Hyperbolic Systems of Equations. Comm. Pure Appl. Maths., vol. 18, 1965, p. 697-715. | MR 194770 | Zbl 0141.28902

[13] T.Y. Hou, Homogenization for Semilinear Hyperbolic Systems with Oscillatory Data. Comm. Pure Appl. Maths., vol. 41, 1988, p. 471-495. | MR 933232 | Zbl 0632.35039

[14] E. Isaacson et B. Temple, The Structure of Asymptotic States in a Singular System of Conservation Laws (à paraître). | Zbl 0717.35053

[15] J.L. Joly, Sur la propagation des oscillations par un système hyperbolique semi-linéaire en dimension 1 d'espace, C.R. Acad. Sci. Paris, t. 296, série I, 1983, p. 669-672. | MR 705687 | Zbl 0555.35081

[16] B.L. Keyfitz et H.C. Kranzer, A System of Non-Strictly Hyperbolic Conservation Laws Arising in Elasticity Theory, Arch. Rat. Mech. Anal., vol. 72, 1980, p. 219-241. | MR 549642 | Zbl 0434.73019

[17] S.N. Kruzkov, First Order Quasilinear Equations in Several Independent Variables, Mat. Sbornik, vol. 81, 1970, p. 217-243. | MR 267257 | Zbl 0215.16203

[18] P.D. Lax, Hyperbolic Systems of Conservation Laws. II, Comm. Pure Appl. Maths., vol. 10, 1957, p. 537-566. | MR 93653 | Zbl 0081.08803

[19] P.D. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, S.I.A.M. series, 1973, Philadelphia. | MR 350216 | Zbl 0268.35062

[20] D. Mclaughlin, G. Papanicolaou et L. Tartar, Weak Limits of Semi-Linear Hyperbolic Systems with Oscillating Data, Macroscopic Modelling of turbulent flows, Nice, 1984. Lect. Notes Phys., n° 230, p. 277-298, Springer-Verlag, Heidelberg. | MR 815927 | Zbl 0588.76137

[21] F. Murat, Compacité par compensation, Ann. Scuola Norm. Pisa, cl. di Sc., série IV, vol. 5, 1978, p. 489-507. | Numdam | MR 506997 | Zbl 0399.46022

[22] F. Murat, L'injection du cône positif de H-1 dans W-1,q est compacte pour tout q < 2, J. Math. Pures et Appl., t. 60, 1981, p. 309-322. | Zbl 0471.46020

[23] R.L. Pego et D. Serre, Instabilities in Glimm's Scheme for Two Systems of Mixed Type, S.I.A.M. J. Num. Anal., vol. 25, 1988, p. 965-988. | MR 960860 | Zbl 0663.73010

[24] M. Rascle et D. Serre, Compacité par compensation et systèmes hyperboliques de lois de conservation. Applications, C.R. Acad. Sci., Paris, t. 299, série I, 1984, p. 673-676. | MR 770461 | Zbl 0578.35056

[25] D.A. Saville et O.A. Palusinski, Theory of Electrophoretic Separations, Parts 1 et 2, A.I.C.H.E. J., vol. 32, 1986.

[26] S. Schochet, Examples of Measure-valued Solutions. Comm. in PDEs, vol. 14, 1989, p. 545-575. | MR 993820 | Zbl 0682.35068

[27] D. Serre, Systèmes hyperboliques riches de lois de conservation, Collège de France, Seminar X. Pitman Res. Notes Math. Ser., Longman (à paraitre). | Zbl 0870.35067

[28] D. Serre, Large Oscillations in Hyperbolic Systems of Conservation Laws, Rend. Sem. Mat., Univ. Pol. Torino, Fascicolo speciale 1988, Hyperbolic equations, 1987, p. 185-201. | MR 1007376 | Zbl 0678.35066

[29] D. Serre, Propagation des oscillations dans les systèmes hyperboliques non linéaires, Nonlinear Hyperbolic Problems, Proceedings, Saint-Étienne, 1986, Lecture Notes in Maths, n° 1270, Springer-Verlag, 1987. | MR 910121 | Zbl 0653.35056

[30] D. Serre, Domaines invariants pour les systèmes hyperboliques de lois de conservation. J. Diff. Eq., 69, 1987, p. 46-62. | MR 897440 | Zbl 0626.35061

[31] D. Serre, Les ondes planes en électromagnétisme non linéaire, Physica D, vol. 31, 1988, p. 227-251. | MR 955629 | Zbl 0736.35133

[32] D. Serre, Un système hyperbolique non linéaire avec des données oscillantes, C.R. Acad. Sci., Paris, t. 302, série I, 1986, p. 115-168. | MR 830281 | Zbl 0606.35050

[33] D. Serre, Solutions à variation bornée pour certains systèmes hyperboliques de lois de conservation, J. Diff. Eq., vol. 68, 1987, p. 137-168. | MR 892021 | Zbl 0627.35062

[34] D. Serre, La compacité par compensation pour les systèmes hyperboliques non linéaires de deux équations à une dimension d'espace, J. Math. Pures et Appl., t. 65, 1986, p. 423-468. | MR 881690 | Zbl 0601.35070

[35] D. Serre, Compacité par compensation et systèmes hyperboliques de lois de conservation, C.R. Acad. Sci., Paris, t. 299, série I, 1984, p. 555-558. | MR 770445 | Zbl 0578.35055

[36] D. Serre, Richness and the Classification of Quasilinear Hyperbolic systems, I.M.A. volumes in Mathematics and its applications n° 29, J. GLIMM & A. MAJDA éds., Springer-Verlag, Heidelberg. | Zbl 0760.35028

[37] D. Serre, Systèmes d'EDO invariants sous l'action de systèmes hyperboliques d'EDPs, Ann. Inst. Fourier, vol. 39, 1989, p. 953-968. | Numdam | MR 1036339 | Zbl 0687.35006

[38] L. Tartar, Compensated Compactness and Applications to PDEs, Nonlinear Analysis et Mechanics, Herriot Watt Symposium, 1979, Pitman Res. Notes Maths. | MR 584398 | Zbl 0437.35004

[39] L. Tartar, Cours Peccot, Collège de France, non publié.

[40] B. Temple, Systems of Conservation Laws with Invariant Submanifolds, Trans. A.M.S., vol. 280, 1983, p. 781-795. | MR 716850 | Zbl 0559.35046

[41] T.D. Venttsel', Estimates of Solutions of the One-Dimensional System of Equations of Gas Dynamics With "Viscosity" Not Depending on "Viscosity", J. Soviet Maths., vol. 31, 1985, p. 3148-3153. | Zbl 0575.76076

[42] D.H. Wagner, Equivalence of the Euler and Lagrangian Equations of Gas Dynamics for Weak Solutions, J. Diff. Eq., vol. 68, 1967, p. 118-136. | MR 885816 | Zbl 0647.76049

[43] J. Duchon et R. Robert, Élargissement diphasique d'une nappe tourbillonaire en dynamique du fluide parfait incompressible, Preprint, Equipe d'Analyse Numérique Lyon-I, n° 64, 1987. | MR 917601