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Blockage hydrodynamics of one-dimensional driven conservative systems. (English) Zbl 1079.60076

Author’s abstract: We consider an arbitrary one-dimensional conservative particle system with finite-range interactions and finite site capacity, governed on the hydrodynamic scale by a scalar conservation law with Lipshitz-continuous flux \(h\). A finite-size perturbation restricts the local current to some maximum value \(\varphi\). We show that the perturbed hydrodynamic behaviour is entirely determined by \(\varphi\) if \(\inf (h;\varphi)\) is first non-decreasing and then non-increasing, which we believe is a necessary condition.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
82C22 Interacting particle systems in time-dependent statistical mechanics
35L65 Hyperbolic conservation laws
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