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Article
Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws
JOURNAL OF STATISTICAL PHYSICS
  • MA Katsoulakis, University of Massachusetts - Amherst
  • AE Tzavaras
Publication Date
1999
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
Citation Information
MA Katsoulakis and AE Tzavaras. "Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws" JOURNAL OF STATISTICAL PHYSICS Vol. 96 Iss. 3-4 (1999)
Available at: http://works.bepress.com/markos_katsoulakis/18/