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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Kinetic Relation
Lattice Model
Traveling Wave Solutions
Phase Transition
Phase transitions
Kinetics
Wave Speed
Traveling Wave
Tail
Jump
Energy
Interaction
Family

Cite this

Kinetic relations for a lattice model of phase transitions. / Schwetlick, Hartmut; Zimmer, Johannes.

In: Archive for Rational Mechanics and Analysis, Vol. 206, No. 2, 01.11.2012, p. 707-724.

Research output: Contribution to journalArticle

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