Kinetic Relations for a Lattice Model of Phase Transitions

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.