On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws

Michel Rascle

Annales de l'I.H.P. Analyse non linéaire (1991)

  • Volume: 8, Issue: 3-4, page 333-350
  • ISSN: 0294-1449

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Rascle, Michel. "On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws." Annales de l'I.H.P. Analyse non linéaire 8.3-4 (1991): 333-350. <http://eudml.org/doc/78257>.

@article{Rascle1991,
author = {Rascle, Michel},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {dynamic of oscillations; separation of the wave cone; hyperbolic system; compensated compactness; characteristics; gas dynamics in Eulerian coordinates; constitutive manifold},
language = {eng},
number = {3-4},
pages = {333-350},
publisher = {Gauthier-Villars},
title = {On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws},
url = {http://eudml.org/doc/78257},
volume = {8},
year = {1991},
}

TY - JOUR
AU - Rascle, Michel
TI - On the static and dynamic study of oscillations for some nonlinear hyperbolic systems of conservation laws
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1991
PB - Gauthier-Villars
VL - 8
IS - 3-4
SP - 333
EP - 350
LA - eng
KW - dynamic of oscillations; separation of the wave cone; hyperbolic system; compensated compactness; characteristics; gas dynamics in Eulerian coordinates; constitutive manifold
UR - http://eudml.org/doc/78257
ER -

References

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  1. [1] J.M. Ball, A Version of the Fundamental Theorem for Young Measures, in PDEs and Continuum Models of Phase Transitions, M. RASCLE, D. SERRE and M. SLEMROD Ed., SpringerLecture Notes in Physics, No. 344, pp. 207-216. Zbl0991.49500MR1036070
  2. [2] Chen Gui-Qiang, Propagation and Cancellation of Oscillations for Hyperbolic Systems of Conservation laws, Preprint, 1990. Zbl0727.35085MR1077915
  3. [3] C.M. Dafermos, Heriot Watt Symposium, 1979, R. J. KNOPS, Ed., Res. Notes in Math., Nonlinear Analysis and Mechanics, Vol. 1, Pitman. Zbl0393.00005MR481581
  4. [4] R.J. Diperna, Convergence of Approximate Solutions to Conservation Laws, Arch. Rat. Mech. Anal., 8, Vol. 82, 1983, pp. 27-70. Zbl0519.35054MR684413
  5. [5] R.J. Diperna, Measure-Valued Solutions to Conservation Laws, Arch. Rat. Mech. Anal., Vol. 88, 1985, pp. 223-270. Zbl0616.35055MR775191
  6. [6] R.J. Diperna, Compensated Compactness and General Systems of Conservation Laws. Zbl0555.35087
  7. [7] P. Gerard, Compacité par compensation et régularité 2-microlocale. Preprint. Zbl0707.35032
  8. [8] F. Murat, L'injection du cône positif de H- dans W-1, q est compacte pour tout q &lt; 2, J. Math. Pures et Appl., T. 60, 1981, pp. 309-322. Zbl0471.46020
  9. [9] M. Rascle, Perturbations par viscosité de certains systèmes hyperboliques non linéaires, Thèse, Lyon, 1983. 
  10. [10] M. Rascle,On the Convergence of the Viscosity Method for the System of Nonlinear 1-D Elasticity, in A.M.S.Lectures in Applied Math., Vol. 23, 1986, pp. 359-377. Zbl0596.35083MR837686
  11. [11] D. Serre, La compacité par compensation pour les systèmes non linéaires de deux équations à une dimension d'espace, J. Maths. Pures Appl., T. 65, 1987, pp. 423-468. Zbl0601.35070MR881690
  12. [12] D. Serre, Oscillations non linéaires des systèmes hyperboliques. Méthodes et résultats qualitatifs, this issue. Zbl0810.35060
  13. [13] L. Tartar, Compensated Compactness and Applications to Partial Differential Equations, in Heriot Watt Symposium, 1979, R. J. KNOPS Ed., Res. Notes in Math., Nonlinear Analysis and Mechanics, No. 4, Pitman. Zbl0437.35004MR584398
  14. [14] L. TartarH-Measures, a New Approach for Studying Homogenization and Concentration Effects in Partial Differential Equations, Preprint. 
  15. [15] D. Wagner, Equivalence of the Euler and Lagrangian Equations of Gas Dynamics for Weak Solutions, J. Diff. Eqs., Vol. 68, 1987, pp. 118-136. Zbl0647.76049MR885816
  16. [16] L.C. Young, Lectures on the Calculus of Variations and Optimal Control Theory, Saunders, Philadelphia, 1969. Zbl0177.37801MR259704

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