Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity

A linear system of differential equations describing the joint motion of a thermoelastic porous body and an incompressible thermofluid occupying a porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main differential equations involve non-smooth rapidly oscillating coefficients, inside the differentiatial operators. A rigorous substantiation based on Nguetseng's two-scale convergence method is carried out for the procedure of the derivation of homogenized equations (not containing rapidly oscillating coefficients), which for different combinations of the physical parameters can represent Biot's system of equations of thermo-poroelasticity, the system consisting of Lame's non-isotropic equations of thermoelasticity for the solid component and the acoustic equations for the fluid component of a two-temperature two-velocity continuum, or Lame's non-isotropic thermoelastic system for a two-temperature one-velocity continuum.