Archive for Rational Mechanics and Analysis

, Volume 206, Issue 2, pp 707–724 | Cite as

Kinetic Relations for a Lattice Model of Phase Transitions

  • Hartmut Schwetlick
  • Johannes Zimmer


The aim of this article is to analyse travelling waves for a lattice model of phase transitions, specifically the Fermi–Pasta–Ulam chain with piecewise quadratic interaction potential. First, for fixed, sufficiently large subsonic wave speeds, we rigorously prove the existence of a family of travelling wave solutions. Second, it is shown that this family of solutions gives rise to a kinetic relation which depends on the jump in the oscillatory energy in the solution tails. Third, our constructive approach provides a very good approximate travelling wave solution.


Lattice Model Wave Speed Travel Wave Solution Entropy Inequality Oscillatory Energy 
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 2012

Authors and Affiliations

  1. 1.Mathematical SciencesUniversity of BathBathUK

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