Euler hydrodynamics of one-dimensional attractive particle systems

Details Euler hydrodynamics of one-dimensional attractive particle systems Euler hydrodynamics of one-dimensional attractive particle systems

2006-09-21

arxiv.org/abs/math/0609605v1

Annals of Probability 2006, Vol. 34, No. 4, 1339-1369

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117906000000115 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117906000000115

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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