Pré-Publication, Document De Travail Année : 2025

Hydrodynamics and relaxation limit for multilane exclusion process and related hyperbolic systems

Gideon Amir
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Ofer Busani
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Ellen Saada
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Résumé

We investigate the hydrodynamic behavior and local equilibrium of the multilane exclusion process, whose invariant measures were studied in our previous paper [1]. The dynamics on each lane follows a hyperbolic time scaling, whereas the interlane dynamics has an arbitrary time scaling. We prove the following: (i) the hydrodynamic behavior of the global density (i.e. summed over all lanes) is governed by a scalar conservation law; (ii) the latter, as well as the limit of individual lanes, is the relaxation limit of a weakly coupled hyperbolic system of balance laws that approximates the particle system. For the hydrodynamic limit, to highlight new phenomena arising in our model, a precise computation of the flux function, with the transitions between different possible shapes (and a physical interpretation thereof), is given for the two-lane model.
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hal-04921506 , version 1 (03-02-2025)

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Gideon Amir, Christophe Bahadoran, Ofer Busani, Ellen Saada. Hydrodynamics and relaxation limit for multilane exclusion process and related hyperbolic systems. 2025. ⟨hal-04921506⟩
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