On the non-equilibrium states of the crystal lattice
We consider the Cauchy problem for an infinite crystal lattice in Zd, d ≥ 1, with random initial data. We study the behavior of the distributions of the solutions as t → ∞.
The main goal is to find the limiting stationary non-equilibrium states in which there is a constant non-zero heat flux passing through the lattice.
non-equilibrium states, crystal lattice, Cauchy problem, random initial data, weak convergence of measures, Gibbs measures, energy current density
Mathematical problems and theory of numerical methods