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Kinetic Relations for a Lattice Model of Phase Transitions

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Abstract

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.

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  1. Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK

    Hartmut Schwetlick & Johannes Zimmer

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  1. Hartmut Schwetlick
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  2. Johannes Zimmer
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Correspondence to Johannes Zimmer.

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Communicated by K. Bhattacharya

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Schwetlick, H., Zimmer, J. Kinetic Relations for a Lattice Model of Phase Transitions. Arch Rational Mech Anal 206, 707–724 (2012). https://doi.org/10.1007/s00205-012-0566-8

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