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.
Pages
715-763
Volume
96
Issue
3-4
Recommended Citation
Katsoulakis, MA and Tzavaras, AE, "Multiscale analysis for interacting particles: Relaxation systems and scalar conservation laws" (1999). JOURNAL OF STATISTICAL PHYSICS. 473.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/473
Comments
The published version is located at http://www.springerlink.com/content/hvr22h175447p9j1/