Kinetic Approach to Systems of Conservation Laws

B. Perthame

Publications mathématiques et informatique de Rennes (1992)

  • Issue: 1, page 192-204

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Perthame, B.. "Kinetic Approach to Systems of Conservation Laws." Publications mathématiques et informatique de Rennes (1992): 192-204. <http://eudml.org/doc/274888>.

@article{Perthame1992,
author = {Perthame, B.},
journal = {Publications mathématiques et informatique de Rennes},
language = {eng},
number = {1},
pages = {192-204},
publisher = {Département de Mathématiques et Informatique, Université de Rennes},
title = {Kinetic Approach to Systems of Conservation Laws},
url = {http://eudml.org/doc/274888},
year = {1992},
}

TY - JOUR
AU - Perthame, B.
TI - Kinetic Approach to Systems of Conservation Laws
JO - Publications mathématiques et informatique de Rennes
PY - 1992
PB - Département de Mathématiques et Informatique, Université de Rennes
IS - 1
SP - 192
EP - 204
LA - eng
UR - http://eudml.org/doc/274888
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. Zbl0549.35078
  2. [Br] Y. Brenier, Résolution d'équations d'évolution quasilinéaires. J. Diff. Eq.50(3), (1986), 375-390. Zbl0549.35055MR723577
  3. [Ce] C. Cercignani. The Boltzmann Equation and its applications. Applied Math. Sc.67, Springer Verlag, Berlin (1988). Zbl0646.76001MR1313028
  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. Zbl0519.35054MR684413
  6. [DLM] R. Di Perna, P.L. Lions, Y. Meyer, LP regularity of velocity averages. A Paraître dans Ann. IHP Anal. Non Lin., 1991. Zbl0763.35014MR1127927
  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. Zbl0652.47031MR923047
  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). Zbl0268.35062MR350216
  10. [LP] P.L. Lions, B. Perthame. Moments, averaging and dispersion lemmas. C.R. Ac. Sc.Paris (1992) to appear. Zbl0761.35085MR1166050
  11. [LPT1] P.L. Lions, B. Perthame, E. Tadmor, Kinetic formulation of scalar conservation laws. Note C.R.A.S. t. Série 1 (1991). Zbl0820.35094
  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. Zbl0717.35017MR1078593
  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-VerlagNew York, Heidelberg-Berlin, (1982). Zbl0807.35002MR1301779
  16. [T] L. Tartar, In Research notes in Mathematics, 39, Henriot-Watt Symp. Vol. 4Pitman Press Boston, London (1975), 136-211. Zbl0437.35004

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