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.
Original languageEnglish
Pages (from-to)707-724
Number of pages18
JournalArchive for Rational Mechanics and Analysis
Volume206
Issue number2
DOIs
Publication statusPublished - 1 Nov 2012

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