The Vlasov approximation for phonon gas

The Vlasov equation is constructed for a collisionless phonon gas in an anisotropic cubic crystal. An equation of Boltzmann type is proposed in the approximation of the collisional relaxation of phonons to the equilibrium distribution. It is shown that in the thermodynamic limit the kinetic model transforms in the thermoelasticity equations. The relationship between the kinetic model of a phonon gas and the Katteneo equation is considered.