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Estimées d’$\varepsilon $-entropie pour les lois de conservation scalaires
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 20, 13 p., doi: 10.5802/slsedp.15
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Résumé - 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.
Bibliography
[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 481581 | Zbl 0373.35048
[3] Dafermos C. M., Hyperbolic conservation laws in continuum physics, Grundlehren Math. Wissenschaften Series, Vol. 325, Springer Verlag, 2000. MR 1763936 | Zbl 0940.35002
[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 2142881 | Zbl 1079.35066
[5] DiPerna R.J., Compensated compactness and general systems of conservation laws, Trans. Amer. Math. Soc. 292 (1985), no. 2, 383–420. MR 808729 | Zbl 0606.35052
[6] Glimm J., Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 (1965), 697–715. MR 194770 | Zbl 0141.28902
[7] Glimm J., Lax P. D., Decay of solutions of nonlinear hyperbolic conservation laws. Mem. Amer. Math. Soc., 101 (1970). MR 265767 | Zbl 0204.11304
[8] Goatin P., Gosse L., Decay of positive waves for $n \times n$ hyperbolic systems of balance laws. Proc. Amer. Math. Soc. 132 (2004), no. 6, 1627–1637. MR 2051123 | Zbl 1043.35111
[9] Hoeffding W., Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58 (1963), 13–30. MR 144363 | Zbl 0127.10602
[10] Hopf E., The partial differential equation $u_{t}+uu_{x}=\mu u_{xx}$, Comm. Pure Appl. Math. 3 (1950), 201–230. MR 47234 | Zbl 0039.10403
[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 267257 | Zbl 0215.16203
[12] Lax P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation. Comm. Pure Appl. Math. 7 (1954), 159–193. MR 66040 | Zbl 0055.19404
[13] Lax P. D., Hyperbolic Systems of Conservation Laws II. Comm. Pure Appl. Math. 10 (1957), 537–566. MR 93653 | Zbl 0081.08803
[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 519059 | Zbl 0457.65068
[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 1383202 | Zbl 0853.76077
[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 1284790 | Zbl 0799.35151
[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 94541 | Zbl 0131.31803
[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 2420006 | Zbl 1152.35074