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Kinetic approach to systems of conservation laws
Benoît Perthame
Journées équations aux dérivées partielles (1992), article no. 8, 13 p.
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DOI: 10.5802/jedp.426
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@article{JEDP_1992____A8_0,
     author = {Beno{\^\i}t Perthame},
     title = {Kinetic approach to systems of conservation laws},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {8},
     publisher = {\'Ecole polytechnique},
     year = {1992},
     doi = {10.5802/jedp.426},
     language = {en},
     url = {https://jedp.centre-mersenne.org/articles/10.5802/jedp.426/}
}
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Benoît Perthame. Kinetic approach to systems of conservation laws. Journées équations aux dérivées partielles (1992), article  no. 8, 13 p. doi : 10.5802/jedp.426. https://jedp.centre-mersenne.org/articles/10.5802/jedp.426/
  • References
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[Br] Y. Brenier, Résolution d'équations d'évolution quasilinéaires. J. Diff. Eq. 50(3), (1986), 375-390. | MR: 85f:35117 | Zbl: 0549.35055

[Ce] C. Cercignani. The Boltzmann Equation and its applications. Applied Math. Sc. 67, Springer Verlag, Berlin (1988). | MR: 95i:82082 | Zbl: 0646.76001

[Ch] C. Q. Chen. The compensated compactness method and the system of isentropic gas dynamics. Preprint MSRI - 00527-91, Mathematical Sciences Research Institute, Berkeley (1990).

[DP] R. J. Di Perna. Convergence of approximate solutions to conservation laws. Arch. Rat. Mech. Anal. 82 (1983) pp. 27-70. | MR: 84k:35091 | Zbl: 0519.35054

[DLM] R. Di Perna, P. L. Lions, Y. Meyer, Lp regularity of velocity averages. A Paraître dans Ann. IHP Anal. Non Lin., 1991. | Numdam | MR: 92g:35036 | Zbl: 0763.35014

[GLPS] F. Golse, P.L. Lions, B. Perthame, R. Sentis, Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76(1), (1988), 11°-125. | MR: 89a:35179 | Zbl: 0652.47031

[K] S. Kruzkov, First order quasi-linear equations with several space variables. Math. USSR Sb. 10 (1970), 217-273.

[L] P.D. Lax. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. CBMS-NSF conference n° 11, SIAM, Philadelfia (1973). | MR: 50 #2709 | Zbl: 0268.35062

[LP] P.L. Lions, B. Perthame. Moments, averaging and dispersion lemmas. C.R. Ac. Sc. Paris (1992) to appear. | Zbl: 0761.35085

[LPT1] P.L. Lions, B. Perthame, E. Tadmor, Kinetic formulation of scalar conservation laws. Note C.R.A.S. t. Série 1 (1991). | Zbl: 0729.49007

[LPT2] P.L. Lions. B. Perthame, E. Tadmor. Kinetic formulation of isentropic gas dynamics in preparation. | Zbl: 0799.35151

[P] B. Perthame, Higher moments for kinetic equations ; Applications to Vlasov-Poisson and Fokker-Planck Equations. Math. Methods in the Appl. Sc. 13(1990), 441-452. | MR: 91j:82044 | Zbl: 0717.35017

[PT] B. Perthame, E. Tadmor, A kinetic equation with kinetic entropy functions for scalar conservation laws. A paraître dans Comm. in Math. Phys. | Zbl: 0729.76070

[S] J. Smoller, Shock waves and reaction diffusion equations. Springer-Verlag New York, Heidelberg-Berlin, (1982).

[T] L. Tartar, In Research notes in Mathematics, 39, Henriot-Watt Symp. Vol. 4 Pitman Press Boston, London (1975), 136-211. | MR: 81m:35014 | Zbl: 0437.35004

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