Strong hydrodynamic limit for attractive particle systems on Z
Résumé
We consider attractive irreducible conservative particle systems on Z, with at most K particles per site, for which no explicit invariant measures are required. We suppose that jumps have a finite positive first moment. In Bahadoran et al. (2006) we proved, under finite range hypothesis, that for such systems the hydrodynamic limit under Euler scaling exists, and is given by the entropy solution of a scalar conservation law with Lipschitz-continuous flux. Here, by a refinement of our method, we obtain an almost sure hydrodynamic limit, when starting from: i) any shock profile (Riemann hydrodynamics); ii) any general initial profile, but with finite range assumption.