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

Markos A. Katsoulakis*, Athanasios E. Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)715-763
Number of pages49
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - Aug 1999
Externally publishedYes


  • Correlation function method
  • Interacting particle systems
  • Multiple scales
  • Rates of convergence
  • Relaxation systems
  • Scalar conservation laws
  • Semidiscrete schemes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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