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Euler Hydrodynamics of One-Dimensional Attractive Particle Systems

C. Bahadoran, H. Guiol, K. Ravishankar and E. Saada
The Annals of Probability
Vol. 34, No. 4 (Jul., 2006), pp. 1339-1369
Stable URL: http://www.jstor.org/stable/25449912
Page Count: 31
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Euler Hydrodynamics of One-Dimensional Attractive Particle Systems
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Abstract

We consider attractive irreducible conservative particle systems on ${\Bbb Z}$, 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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