Multiscale analysis for interacting particles: Relaxation systems and scalar conservation lawsJOURNAL OF STATISTICAL PHYSICS
AbstractWe 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.
Citation InformationMA 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/