Euler hydrodynamics of one-dimensional attractive particle systems

Annals of Probability

Volumn 34, Issue 4, 2006, Pages 1339-1369

  Bahadoran, C ^a   Guiol, H ^b   Ravishankar, K ^c   Saada, E ^d  

^a UNIVERSITÉ CLERMONT AUVERGNE   (France)

^b GRENOBLE INSTITUTE OF TECHNOLOGY   (France)

^c STATE UNIVERSITY OF NEW YORK   (United States)

^d CNRS   (France)

Author keywords

Attractive particle system; Entropy solution; Glimm scheme; Hydrodynamics; Nonconvex or nonconcave flux; Nonexplicit invariant measures

Indexed keywords

EID: 33750168878     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000115     Document Type: Article

References (26)

1. ANDJEL, E. D. (1982). Invariant measures for the zero range process. Ann. Probab. 10 525-547. MR0659526
2. ANDJEL, E. D. and VARES, M. E. (1987). Hydrodynamic equations for attractive particle systems on ℤ. J. Statist. Phys. 47 265-288. MR0892931
3. BAHADORAN, C. (2004). Blockage hydrodynamics of one-dimensional driven conservative systems. Ann. Pmbab. 32 805-854. MR2039944
4. BRAMSON, M. and MOUNTFORD, T. (2002). Stationary blocking measures for onedimensional nonzero mean exclusion processes. Ann. Probab. 30 1082-1130. MR1920102
5. BAHADORAN, C., GUIOL, H., RAVISHANKAR, K. and SAADA, E. (2002). A constructive approach to Euler hydrodynamics for attractive particle systems. Application to k-step exclusion. Stochastic Process. Appl. 99 1-30. MR1894249
6. BRESSAN, A. (2000). Hyperbolic Systems of Conservation Laws: The One-Dimensional Cauchy Problem. Oxford Univ. Press. MR1816648
7. ℤd. Rapport du laboratoire de probabilités, Univ. Paris VI.
8. COCOZZA-THIVENT, C. (1985). Processus des misanthropes. Z. Wahrsch. Verw. Gebiete 70 509-523. MR0807334
9. EKHAUS, M. and GRAY, L. (1994). Convergence to equilibrium and a strong law for the motion of restricted interfaces. Unpublished manuscript.
10. GLIMM, J. (1965). Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 18 697-715. MR0194770
11. GODLEWSKI, E. and RAVIART, P. A. (1991). Hyperbolic Systems of Conservation Laws. Ellipses, Paris. MR1304494
12. GUIOL, H. (1999). Some properties of k-step exclusion processes. J. Statist. Phys. 94495-511. MR 1675362
13. KEISLING, J. D. (1998). An ergodic theorem for the symmetric generalized exclusion process. Markov Process. Related Fields 4 351 -379. MR1670031
14. KIPNIS, C. and LANDIM, C. (1999). Scaling Limits of Interacting Particle Systems. Springer, Berlin. MR1707314
15. KRUŽKOV, S. N. (1970). First order quasilinear equations with several independent variables. Math. URSS Sb. 10217-243.
16. LANDIM, C. (1993). Conservation of local equilibrium for attractive particle systems on ℤd. Ann. Probab. 21 1782-1808. MR1245290
17. LAX, P. D. (1957). Hyperbolic systems of conservation laws II. Comm. Pure Appl. Math. 10 537-566. MR0093653
18. LIGGETT, T. M. (1976). Coupling the simple exclusion process. Ann. Probab. 4 339-356. MR0418291
19. LIGGETT, T. M. (1985). Interacting Particle Systems. Springer, New York. MR0776231
20. REZAKHANLOU, F. (1991). Hydrodynamic limit for attractive particle systems on ℤd. Comm. Math. Phys. 140 417-448. MR1130693
21. REZAKHANLOU, F. (2001). Continuum limit for some growth models. II. Ann. Probab. 29 1329-1372. MR1872745
22. ROCKAFELLAR, R. T. and WETS, R. J.-B. (1998). Variational Analysis. Springer, Berlin. MR1491362
23. SEPPÄLÄINEN, T. (1999). Existence of hydrodynamics for the totally asymmetric simple K-exclusion process. Ann. Probab. 27 361-415. MR1681094
24. SEPPÄLÄINEN, T. (2006). Translation Invariant Exclusion Processes. Available at http://www. math.wisc.edu/~seppalai/excl-book/etusivu. html.
25. SERRE, D. (1999). Systems of Conservation Laws. 1. Hyperbolicity, Entropies, Shock Waves. (Translated from the 1996 French original by I. N. Sneddon.) Cambridge Univ. Press. MR1707279
26. VOL'PERT, A. I. (1967). The spaces BV and quasilinear equations. Math. Sb. (N.S.) 73 (115) 225-302. MR0216338