TY - JOUR
T1 - Kinetic Relations for a Lattice Model of Phase Transitions
AU - Schwetlick, Hartmut
AU - Zimmer, Johannes
PY - 2012/11
Y1 - 2012/11
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84870313396&partnerID=8YFLogxK
U2 - 10.1007/s00205-012-0566-8
DO - 10.1007/s00205-012-0566-8
M3 - Article
AN - SCOPUS:84870313396
SN - 0003-9527
VL - 206
SP - 707
EP - 724
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -