Propagation and conditional propagation of chaos for pressureless gas equations

Probability Theory and Related Fields

Volumn 126, Issue 4, 2003, Pages 459-476

  Dermoune, Azzouz ^a  

^a UFR de Mathematiques Pures et Appliquees   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042333217     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0274-2     Document Type: Article

References (21)

1. Agarwal, R.K., Halt, D.W.: A modified CUSP scheme in wave/particle split form for unstructured grid Euler flows. In 'Frontiers of Computational Fluif Dynamics, D.A. Caughey and M.M. Hafos, eds., Wiley, 1994
2. Baraille, R., Bourdin, G., Dubois, F., Le Roux, A.Y.: Une version à pas fractionnaires du schèma de Godunov pour l'hydrodynamique. C.R. Acad. Sci. Paris, t. 314, Série 1, 147-152 (1992)
3. Barlow, M. T., Yor, M.: Semi-martingale Inequalities via the Garsia-Rodemich-Rumsey Lemma, and Applications to Local Times. J. Functional Analysis 49, 198-229 (1982)
4. Brenier, Y., Grenier, E.: Sticky particles and scalar conservation laws. SIAM J. Numer. Anal. 35, 2317-2328 (1998)
5. Carnevale, G.F., Pomeau, Y., Young, W.R.: Statistics of ballistic agglomeration. Phys. Rev. Lett. 64, no 24, 2913 (1990)
6. Chow, Y.S., Teicher, H.: Probability theory. Springer, New York. 1978
7. Dermoune, A.: Probabilistic interpretation of sticky particle model. The Annals of Probability 1999, 27(3), 1357-1367 (1999)
8. Dermoune, A., Djehiche, B.: Pressureless gas equations with viscosity and nonlinear diffusion. C. R. Acad. Sci. Paris, t. 332, Série I, 741-750 (2001)
9. Dermoune, A., Djehiche, B.: Global solution of pressureless gas equation with viscosity. Physica D 163, 184-190 (2002)
10. Dermoune, A.: Propagation of chaos for pressureless gas equations. C. R. Acad. Sci. Paris, Ser. I, t. 335, 935-940 (2002)
11. E, W., Rykov, Y., Sinai, Y.: 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, 349-380 (1996)
12. Kofman, L., Pogosyan, D., Shandarin, S.: Structure of the universe in the two-dimensional model of adhesion. Mon. Nat. R. Astr. Soc. 242, 200-208 (1990)
13. Li, Y., Cao, Y.: Large particle difference method with second order accuracy in gas dynamics. Scientific Sinica (A) 28, 1024-1035 (1985)
14. Oelshläger K.: A law of large numbers for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 69, 279-322 (1985)
15. Sever, M.: An existence theorem in the large for zero-pressure gas dynamics. Diff. Integral Equations 14(9), 1077-1092 (2001)
16. Stroock, D.W., Varadhan, S.R.S.: Mutidimensional diffusion processes. Springer New York, 1979
17. Sznitman, A.S.: A propagation of chaos results for burgers' equation. Probab. Th. Rel. Fields 71, 581-613 (1986)
18. Sznitman A.S.: Topics in propagation of chaos, École d'Été de Probabilités de Saint-Flours XIX-1989
19. Sznitman A.S.: Equations de type Boltzmann spatialement homogènes. Z. Wahrscheinlichkeitstheor. Verw. Gebiete 66, 559-592 (1984)
20. Shandarin, S., Zeldovich, Y.: The large scale structures of the universe: turbulence, intermittency, structures in a self-gravitating medium. Rev. Mod. Phys. 61, 185-220 (1989)
21. Zheng, W.: Conditional propagation of chaos and a class of quasilinear PDE'S. The Annals of Probability 23(3), 1389-1413 (1995)