Sticky particles and scalar conservation laws

SIAM Journal on Numerical Analysis

Volumn 35, Issue 6, 1998, Pages 2317-2328

  Brenier, Yann ^a   Grenier, Emmanuel ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Conservation laws; Gas dynamics

Indexed keywords

EID: 0001454943     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142997317353     Document Type: Article

References (18)

1. M. BARDI, L. C. EVANS, On Hopf's formulas for solutions of Hamilton-Jacobi equations, Nonlinear Anal. 8 (1984), pp. 1373-1381.
2. F. BOUCHUT, Advances in Kinetic Theory and Computing, Ser. Adv. Math. Appl. Sci. 22, World Scientific, River Edge, NJ, 1994.
3. F. BOUCHUT AND F. JAMES, Equations de transport unidimensionnelles à coefficients discontinus, C. R. Acad. Sci. Paris Sér. I Math., 320 (1995), pp. 1097-1102.
4. Y. BRENIER AND E. GRENIER, On the Model of Pressureless Gases with Sticky Particles, CAM Report 94-45, Univ. of California, Los Angeles, 1994.
5. C. DAFERMOS, Polygonal approximations of solutions of the initial value problem for a conservation law, J. Math. Anal. Appl., 38 (1972), pp. 33-41.
6. W. E, Y. G. RYKOV, AND Y. G. SINAI, Generalized variational principles, global weak solutions and behavior with random initial data for systems of conservation laws arising in adhesion particle dynamics, Comm. Math. Phys., 177 (1996), pp. 349-380.
7. E. GRENIER, Existence globale pour le systhme des gaz sans pression, C. R. Acad. Sci. Paris Sér. I Math., 321 (1995), pp. 171-174.
8. E. GRENIER, Ph.D. thesis, Université Paris VI, 1995.
9. R. J. LEVEQUE, Large time step shock-capturing techniques for scalar conservation laws, SIAM J. Numer. Anal., 19 (1982), pp. 1091-1109.
10. P.-L. LIONS, B. PERTHAME, AND E. TADMOR, A kinetic formulation of multidimensional scalar conservation laws and related equations, J. Amer. Math. Soc., 7 (1994), pp. 169-191.
11. F. POUPAUD AND M. RASCLE, Measure solutions to the linear transport equations with non-smooth coefficients, Comm. Partial Differential Equations, 22 (1997), pp. 337-358.
12. L. SCHWARTZ, Cours d'analyse, Hermann, Paris, 1981.
13. D. SERRE, Systèmes de lois de conservation, I, Diderot, Paris, 1996.
14. ZH. S. SHE, E. AURELL, AND U. FRISCH, Statistics of shocks in solutions of inviscid Burgers equation, Comm. Math. Phys., 148 (1992), pp. 623-641.
15. YA. SINAI, Statistics of shocks in solutions of inviscid Burgers equation, Comm. Math. Phys., 148 (1992), pp. 605-622.
16. J. SILK, A. SZALAY, AND YA. B. ZELDOVICH, Scientific American, 249 (1983), pp. 72-80.
17. A. I. VOLPERT, Spaces BV and quasilinear equations, Mat. Sb. (N.S.), 73 (1967), pp. 255-302 (in Russian).
18. YA. B. ZELDOVICH, Gravitational instability: An approximate theory for large density perturbations, Astro. Astrophys., 5 (1970), p. 84.