Brenier, Y.; Corrias, L.
A kinetic formulation for multi-branch entropy solutions of scalar conservation laws
Annales de l'I.H.P. Analyse non linéaire, Tome 15 (1998) no. 2 , p. 169-190
Zbl 0893.35068 | MR 1614638 | 8 citations dans Numdam
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[B1] Y. Brenier, Résolution d'équation d'évolution quasilinéaires en dimension N d'espace à l'aide d'équations linéaires en dimension N + 1, J. Diff. Equat., Vol. 50. 1983. pp. 375-390 and C.R.A.S., Vol. 292, Série I, 1981. MR 723577 | Zbl 0549.35055

[B2] Y. Brenier, Averaged Multivalued Solution for Scalar Conservation Laws, SIAM J. Numer. Anal., Vol. 21, 1984, pp. 1013-1037. MR 765504 | Zbl 0565.65054

[Br] H. Brezis, Analyse fonctionnelle, Masson, 1987. MR 697382 | Zbl 0511.46001

[C] S. Cordier, PHD dissertation, Ecole Polytechnique, 1994.

[DLM] R.J. Diperma, P.-L. Lions and Y. Meyer, Lp Regularity of Velocity Averages, Ann. Inst. Henri Poincaré, Vol. 8. 1991, pp. 271-287. Numdam | MR 1127927 | Zbl 0763.35014

[DM] L. Desvillettes and S. Mischler, About the Splitting Algorithm for Boltzmann and BGK Equations, preprint.

[EFO] B. Engquist, E. Fatemi and S. Osher, Numerical Solution of the High Frequency Asymptotic Expansion for Hyperbolic Equation, proc. ACES Conference, Applied Computational Electromagnetism, ACES, 1994, pp. 32-44.

[FF] A. Forestier and Ph. Le Floch, Multivalued Solutions to Some Non-Linear and Non-Strictly Hyperbolic Systems, Japan J. Ind. Appl. Math., Vol. 9, 1992, pp. 1-23. MR 1153771 | Zbl 0768.35058

[G] H. Grad, On the Kinetic Theory of Rarefied Gases, Coom. Pure and Appl. Math., Vol. 2, 1949, pp. 331-404. MR 33674 | Zbl 0037.13104

[GLPS] F. Golse, P.-L. Lions, B. Perthame, R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal., Vol. 76, 1988, pp. 110-125. MR 923047 | Zbl 0652.47031

[GM] Y. Giga and T. Miyakawa, A Kinetic Construction of Global Solutions of First Order Quasilinear Equations, Duke Math. J., Vol. 50, 1983, pp. 505-515. MR 705037 | Zbl 0519.35053

[KN] M.G. Krein and A.A. Nudelman, The Markov moment problem, AMS, Providence, 1977.

[L] D. Levermore, Moment Closure of the Boltzmann Equations, preprint 1994.

[LPT1] P.-L. Lions, B. Perthame and E. Tadmor, A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations, J. A.M.S., Vol. 7, 1994, pp. 169-191. MR 1201239 | Zbl 0820.35094

[LPT2] P.-L. Lions, B. Perthame and E. Tadmor, Kinetic Formulation of the Isentropic Gas Dynamics and p-Systems, Comm. Math. Phys., Vol. 163, 1994, pp. 415-431. MR 1284790 | Zbl 0799.35151

[TS] J. Van Trier and W. Symes, Upwind Finite Difference Calculations of Travel Times, Geophysics, Vol. 56, 1991, pp. 812-821.