Equations of nonisothermal filtration in fast processes in elastic porous media

The problem of the nonisothermal joint motion of an elastic porous body and the fluid filling the pores is considered for the case where the duration of the physical process is fractions of a second. A rigorous derivation of averaged equations (equations not containing fast oscillating coefficients) based on the Nguetseng two-scale convergence method is proposed. For various combinations of physical parameters of the problem, these equations include anisotropic nonisothermal Stokes equations for the velocity of the fluid component and the equations of nonisothermal acoustics for the displacements of the solid component or anisotropic nonisothermal Stokes equations for a single-velocity continuum.