Journal of Statistical Physics

, Volume 38, Issue 3–4, pp 615–645 | Cite as

On the asymptotic behaviour of Spitzer's model for evolution of one-dimensional point systems

  • J. Fritz
Articles

Abstract

A nearest-neighbor gradient dynamics of one-dimensional infinite particle systems is considered; the model admits a two-parameter family of stationary configurations. Some domains of attraction of stationary configurations are described, and the continuum (hydrodynamical) limit of the system is investigated. It is shown that the mean density of points satisfies a nonlinear diffusion equation in the hydrodynamical limit.

Key words

Gradient dynamics local stability lattice approximation hydrodynamical limit 

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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • J. Fritz
    • 1
  1. 1.Mathematical Institute, H.A.S.BudapestHungary

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