Kinetic approach to systems of conservation laws

Benoît Perthame

Journées équations aux dérivées partielles (1992)

  • page 1-13
  • ISSN: 0752-0360

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Perthame, Benoît. "Kinetic approach to systems of conservation laws." Journées équations aux dérivées partielles (1992): 1-13. <http://eudml.org/doc/93260>.

@article{Perthame1992,
author = {Perthame, Benoît},
journal = {Journées équations aux dérivées partielles},
keywords = {kinetic models; conservation laws; hyperbolic system of isentropic gas dynamics},
language = {eng},
pages = {1-13},
publisher = {Ecole polytechnique},
title = {Kinetic approach to systems of conservation laws},
url = {http://eudml.org/doc/93260},
year = {1992},
}

TY - JOUR
AU - Perthame, Benoît
TI - Kinetic approach to systems of conservation laws
JO - Journées équations aux dérivées partielles
PY - 1992
PB - Ecole polytechnique
SP - 1
EP - 13
LA - eng
KW - kinetic models; conservation laws; hyperbolic system of isentropic gas dynamics
UR - http://eudml.org/doc/93260
ER -

References

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  1. [Ba] C. BARDOS. Introduction aux problèmes hyperboliques. In CIME Lesson, LN 1047, Springer Verlag, Berlin. H. B. Da Veiga Editor. Zbl0549.35078MR86k:35082
  2. [Br] Y. BRENIER, Résolution d'équations d'évolution quasilinéaires. J. Diff. Eq. 50(3), (1986), 375-390. Zbl0549.35055MR85f:35117
  3. [Ce] C. CERCIGNANI. The Boltzmann Equation and its applications. Applied Math. Sc. 67, Springer Verlag, Berlin (1988). Zbl0646.76001MR95i:82082
  4. [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). 
  5. [DP] R. J. DI PERNA. Convergence of approximate solutions to conservation laws. Arch. Rat. Mech. Anal. 82 (1983) pp. 27-70. Zbl0519.35054MR84k:35091
  6. [DLM] R. DI PERNA, P. L. LIONS, Y. MEYER, Lp regularity of velocity averages. A Paraître dans Ann. IHP Anal. Non Lin., 1991. Zbl0763.35014MR92g:35036
  7. [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. Zbl0652.47031MR89a:35179
  8. [K] S. KRUZKOV, First order quasi-linear equations with several space variables. Math. USSR Sb. 10 (1970), 217-273. 
  9. [L] P.D. LAX. Hyperbolic systems of conservation laws and the mathematical theory of shock waves. CBMS-NSF conference n° 11, SIAM, Philadelfia (1973). Zbl0268.35062MR50 #2709
  10. [LP] P.L. LIONS, B. PERTHAME. Moments, averaging and dispersion lemmas. C.R. Ac. Sc. Paris (1992) to appear. Zbl0761.35085
  11. [LPT1] P.L. LIONS, B. PERTHAME, E. TADMOR, Kinetic formulation of scalar conservation laws. Note C.R.A.S. t. Série 1 (1991). Zbl0729.49007
  12. [LPT2] P.L. LIONS. B. PERTHAME, E. TADMOR. Kinetic formulation of isentropic gas dynamics in preparation. Zbl0799.35151
  13. [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. Zbl0717.35017MR91j:82044
  14. [PT] B. PERTHAME, E. TADMOR, A kinetic equation with kinetic entropy functions for scalar conservation laws. A paraître dans Comm. in Math. Phys. Zbl0729.76070
  15. [S] J. SMOLLER, Shock waves and reaction diffusion equations. Springer-Verlag New York, Heidelberg-Berlin, (1982). Zbl0508.35002
  16. [T] L. TARTAR, In Research notes in Mathematics, 39, Henriot-Watt Symp. Vol. 4 Pitman Press Boston, London (1975), 136-211. Zbl0437.35004MR81m:35014

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