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Communications in Mathematical Physics

, Volume 86, Issue 3, pp 363–373 | Cite as

Local stability and hydrodynamical limit of Spitzer's one dimensional lattice model

  • J. Fritz
Article

Abstract

An infinite system of ordinary differential equations is considered, the right hand side is just the negative gradient of potential energy of a one-dimensional system of unbounded spins interacting by a symmetric and convex pair potential. Constant configurations are stationary points and the mean spin is conserved. It is shown that each of these stationary points has its own domain of attraction, the initial distribution need not be translation invariant. As a consequence we obtain that the mean spin satisfies the heat equation in the hydrodynamical limit.

Keywords

Neural Network Potential Energy Complex System Ordinary Differential Equation Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • J. Fritz
    • 1
  1. 1.Mathematical InstituteBudapestHungary

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