Estimées d’ε-entropie pour les lois de conservation scalaires
Olivier Glass1
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), Talk no. 20, 13 p.

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.

DOI: 10.5802/slsedp.15
Olivier Glass 1

1 Ceremade Université Paris-Dauphine CNRS UMR 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France 
@article{SLSEDP_2011-2012____A20_0,
     author = {Olivier Glass},
     title = {Estim\'ees d{\textquoteright}$\varepsilon $-entropie pour les lois de conservation scalaires},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:20},
     pages = {1--13},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2011-2012},
     doi = {10.5802/slsedp.15},
     language = {fr},
     url = {https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.15/}
}
TY  - JOUR
AU  - Olivier Glass
TI  - Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires
JO  - Séminaire Laurent Schwartz — EDP et applications
N1  - talk:20
PY  - 2011-2012
SP  - 1
EP  - 13
PB  - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.15/
DO  - 10.5802/slsedp.15
LA  - fr
ID  - SLSEDP_2011-2012____A20_0
ER  - 
%0 Journal Article
%A Olivier Glass
%T Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires
%J Séminaire Laurent Schwartz — EDP et applications
%Z talk:20
%D 2011-2012
%P 1-13
%I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
%U https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.15/
%R 10.5802/slsedp.15
%G fr
%F SLSEDP_2011-2012____A20_0
Olivier Glass. Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 20, 13 p. doi : 10.5802/slsedp.15. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.15/

[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. | MR | Zbl

[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. | MR | Zbl

[3] Dafermos C. M., Hyperbolic conservation laws in continuum physics, Grundlehren Math. Wissenschaften Series, Vol. 325, Springer Verlag, 2000. | MR | Zbl

[4] De Lellis C., Golse F., A Quantitative Compactness Estimate for Scalar Conservation Laws, Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998. | MR | Zbl

[5] DiPerna R.J., Compensated compactness and general systems of conservation laws, Trans. Amer. Math. Soc. 292 (1985), no. 2, 383–420. | MR | Zbl

[6] Glimm J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697–715. | MR | Zbl

[7] Glimm J., Lax P. D., Decay of solutions of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc., 101 (1970). | MR | Zbl

[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. | MR | Zbl

[9] Hoeffding W., Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963), 13–30. | MR | Zbl

[10] Hopf E., The partial differential equation u t +uu x =μu xx , Comm. Pure Appl. Math. 3 (1950), 201–230. | MR | Zbl

[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. | MR | Zbl

[12] Lax P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954), 159–193. | MR | Zbl

[13] Lax P. D., Hyperbolic Systems of Conservation Laws II. Comm. Pure Appl. Math. 10 (1957), 537–566. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

Cited by Sources: