  A generalized Hydrodynamics, referred to as Mesoscopic Hydro-Thermodynamics,
of phonons in semiconductors is presented. It involves the descriptions of the
motion of the quasi-particle density and of the energy density. The
hydrodynamic equations, which couple both types of movement via thermo-elastic
processes, are derived starting with a generalized Peierls-Boltzmann kinetic
equation obtained in the framework of a Non-Equilibrium Statistical Ensemble
Formalism, providing such a Mesoscopic Hydro-Thermodynamics. The case of a
contraction in first order relevant variables is worked out in detail. The
associated Maxwell times are derived and discussed. The densities of
quasi-particles and of energy are found to satisfy coupled
Maxwell-Cattaneo-like hyperbolic equations. The analysis of thermo-elastic
effects is done and applied to investigate thermal distortion in silicon
mirrors under incidence of high intensity X-ray pulses in free electron laser
(FEL) facilities. The derivation of a generalized Guyer-Krumhansl equation
governing the flux of heat and the associated conductivity coefficient is also
presented.
