Estimées d’ ε -entropie pour les lois de conservation scalaires

Olivier Glass[1]

  • [1] Ceremade Université Paris-Dauphine CNRS UMR 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France

Séminaire Laurent Schwartz — EDP et applications (2011-2012)

  • page 1-13
  • ISSN: 2266-0607

Abstract

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Dans cet exposé, on s’intéresse aux lois de conservation scalaires en dimension 1 d’espace, et aux propriétés de compacité associées au semi-groupe qu’elles engendrent.

How to cite

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Glass, Olivier. "Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires." Séminaire Laurent Schwartz — EDP et applications (2011-2012): 1-13. <http://eudml.org/doc/251166>.

@article{Glass2011-2012,
abstract = {Dans cet exposé, on s’intéresse aux lois de conservation scalaires en dimension $1$ d’espace, et aux propriétés de compacité associées au semi-groupe qu’elles engendrent.},
affiliation = {Ceremade Université Paris-Dauphine CNRS UMR 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France},
author = {Glass, Olivier},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {fre},
pages = {1-13},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires},
url = {http://eudml.org/doc/251166},
year = {2011-2012},
}

TY - JOUR
AU - Glass, Olivier
TI - Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2011-2012
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 13
AB - Dans cet exposé, on s’intéresse aux lois de conservation scalaires en dimension $1$ d’espace, et aux propriétés de compacité associées au semi-groupe qu’elles engendrent.
LA - fre
UR - http://eudml.org/doc/251166
ER -

References

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  1. Bartlett P. L., Kulkarni S. R., Posner S. E., Covering numbers for real-valued function classes. IEEE Trans. Inform. Theory 43 (1997), no. 5, 1721–1724. Zbl0947.26008MR1476815
  2. Dafermos C. M., Characteristics in hyperbolic conservation laws. A study of the structure and the asymptotic behaviour of solutions, Nonlinear analysis and mechanics : Heriot-Watt Symposium (Edinburgh, 1976), Vol. I, 1–58. Res. Notes in Math., No. 17, Pitman, London, 1977. Zbl0373.35048MR481581
  3. Dafermos C. M., Hyperbolic conservation laws in continuum physics, Grundlehren Math. Wissenschaften Series, Vol. 325, Springer Verlag, 2000. Zbl0940.35002MR1763936
  4. De Lellis C., Golse F., A Quantitative Compactness Estimate for Scalar Conservation Laws, Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998. Zbl1079.35066MR2142881
  5. DiPerna R.J., Compensated compactness and general systems of conservation laws, Trans. Amer. Math. Soc. 292 (1985), no. 2, 383–420. Zbl0606.35052MR808729
  6. Glimm J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697–715. Zbl0141.28902MR194770
  7. Glimm J., Lax P. D., Decay of solutions of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc., 101 (1970). Zbl0204.11304MR265767
  8. Goatin P., Gosse L., Decay of positive waves for n × n hyperbolic systems of balance laws. Proc. Amer. Math. Soc. 132 (2004), no. 6, 1627–1637. Zbl1043.35111MR2051123
  9. Hoeffding W., Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963), 13–30. Zbl0127.10602MR144363
  10. Hopf E., The partial differential equation u t + u u x = μ u x x , Comm. Pure Appl. Math. 3 (1950), 201–230. Zbl0039.10403MR47234
  11. Kružkov S. N., First order quasilinear equations with several independent variables. Mat. Sb. (N.S.) 81 (123) 1970, 228–255 (en russe). Traduction anglaise dans Math. USSR Sbornik Vol. 10 (1970), No. 2, 217–243. Zbl0215.16203MR267257
  12. Lax P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954), 159–193. Zbl0055.19404MR66040
  13. Lax P. D., Hyperbolic Systems of Conservation Laws II. Comm. Pure Appl. Math. 10 (1957), 537–566. Zbl0081.08803MR93653
  14. Lax P. D., Accuracy and resolution in the computation of solutions of linear and nonlinear equations. Recent advances in numerical analysis (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1978). Publ. Math. Res. Center Univ. Wisconsin, 41, 107–117. Academic Press, New York, 1978. Zbl0457.65068MR519059
  15. Lax P. D., Course on hyperbolic systems of conservation laws. XXVII Scuola Estiva di Fis. Mat., Ravello, 2002. 
  16. Lions P.-L., Perthame B., Souganidis P. E., Existence and stability of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates. Comm. Pure Appl. Math. 49 (1996), no. 6, 599–638. Zbl0853.76077MR1383202
  17. Lions P.-L., Perthame B., Tadmor E., Existence and stability of entropy solutions to isentropic gas dynamics in Eulerian and Lagrangian variables. Comm. Math. Phys. 163 (1994), 415–431. Zbl0799.35151MR1284790
  18. Oleinik O. A., Discontinuous solutions of non-linear differential equations. Uspehi Mat. Nauk (N.S.) 12 (1957) no. 3(75), 3–73 (en russe). Traduction anglaise dans Ann. Math. Soc. Trans. Ser. 2 26, 95–172. Zbl0131.31803MR94541
  19. Robyr R., SBV regularity of entropy solutions for a class of genuinely nonlinear scalar balance laws with non-convex flux function. J. Hyperbolic Differ. Equ. 5 (2008), no. 2, 449–475. Zbl1152.35074MR2420006

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