arXiv math/06096052006-09-21math.PR

Euler hydrodynamics of one-dimensional attractive particle systems

C. Bahadoran, H. Guiol, K. Ravishankar, E. Saada

备注：: Published at http://dx.doi.org/10.1214/009117906000000115 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
发表信息：: Annals of Probability 2006, Vol. 34, No. 4, 1339-1369
DOI：: 10.1214/009117906000000115

英文摘要：

We consider attractive irreducible conservative particle systems on $\mathbb{Z}$, without necessarily nearest-neighbor jumps or explicit invariant measures. We prove that for such systems, the hydrodynamic limit under Euler time scaling exists and is given by the entropy solution to some scalar conservation law with Lipschitz-continuous flux. Our approach is a generalization of Bahadoran et al. [Stochastic Process. Appl. 99 (2002) 1--30], from which we relax the assumption that the process has explicit invariant measures.

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