Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws

Publication Date

1999

Journal or Book Title

JOURNAL OF STATISTICAL PHYSICS

Abstract

We investigate the derivation of semilinear relaxation systems and scalar conservation laws from a class of stochastic interacting particle systems. These systems are Markov jump processes set on a lattice, they satisfy detailed mass balance (but not detailed balance of momentum), and are equipped with multiple scalings. Using a combination of correlation function methods with compactness and convergence properties of semidiscrete relaxation schemes we prove that, at a mesoscopic scale, the interacting particle system gives rise to a semilinear hyperbolic system of relaxation type, while at a macroscopic scale it yields a scalar conservation law. Rates of convergence are obtained in both scalings.

Comments

The published version is located at http://www.springerlink.com/content/hvr22h175447p9j1/

Pages

715-763

Volume

96

Issue

3-4

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