Kinetic Modeling for Transport of Elastic Waves in Anisotropic Heterogeneous Media

This paper deals with the derivation of transport equations for high-frequency elastic bulk waves propagating in anisotropic het- erogeneous media. The former describe the evolution of the energy density associated to those waves in the phase space posi- tion × wave vector. The model accounts for all possible polarization of waves in an anisotropic elastic medium and their inter-actions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide on acoustic axes. Thus it embodies isotropic elasticity which was considered in several previous publications. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators.