Shock profiles for the Perthame-Tadmor kinetic model

Communications in Partial Differential Equations

Volumn 23, Issue 11-12, 1998, Pages 487-500

  Golse, François ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011569735     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309808821405     Document Type: Article

References (16)

1. L. Arkeryd, C. Cercignani, R. Illner, Measure Solutions of the Steady Boltzmann Equation in a Slab: Commun. in Math. Phys. 142. 285-296. (1995).
2. L. Arkeryd, A. Nouri, A Compactness Result Related to the Stationary Boltzmann Equation in a Slab with Application to the Existence Theory; Indiana Univ. Math. J., to appear.
3. C. Bose. R. Illner, S. Ukai. On Shock Wave Solutions for Discrete Velocity Models of the Boltzmann Equation: preprint, (1994).
4. Y. Brenier, Ondes de choc numériques de la méthode de transport et écroulement; Thèse d'Etat, Université Paris IX, (1983).
5. Y. Brenier, Une équation homologique avec contrainte, C. R. Acad. Sci. 295, série I, 103-107, (1982).
6. Y. Brenier, Résolution déquations d'évolution quasi-linéaires en dimension N d'espace à l'aide d'équa-tions linéaires en dimension N + 1; J. of Diff. Eq. 50, 375-390, (1983).
7. R. Caflisch, Navier-Stokes and Boltzmann Shock Profiles for a Model of Gas Dynamics: Comm. on Pure and Appl. Math. 32, 521-554. (1979).
8. R. Caflisch, B. Nicolaenko. Shock Profile Solutions of the Boltzmann Equation; Commun. Math. Phys. 86, 161-194, (1982).
9. Y. Giga, Y. Miyakawa: A Kinetic Construction of Global Solutions of 1st Order Quasilinear Equations: Duke Math. J. 50, 505-515. (1983).
10. F. Golse, P.-L. Lions, B. Perthame, R. Sentis, Regularity of the Moments of the Solution of a Transport Equation; J. of Funct. Anal. 76, 110-125. (1988).
11. P.-L. Lions, B. Perthame, E. Tadmor. A Kinetic Formulation of Multi-dimensional Scalar Conservation Laws and Related Equations: J. of the A.M.S. 7. 169-191, (1994).
12. B. Nicolaenko, J. Thurber, Weak Shock and Bifurcating Solutions of the Nonlinear Boltzmann Equation; J. Mech. 14, 305-338, (1975).
13. B. Perthame, Cours Peccot; Collège de France, (1990).
14. B. Perthame, E. Tadmor, A Kinetic Equation with Kinetic Entropy Functions for Scalar Conservation Laws; Commun. in Math. Phys. 163, 415-431, (1994).
15. J. Smoller, "Shock Waves and Reaction-Diffusion Equations". Springer Verlag (1983).
16. S. Ukai, Stationary Solution of the BGK Model Equation in a Finite Interval with Large Boundary Data; Transport Theory and Stat. Phys. 21 487-500, (1992).