Nonisothermal Filtration and Seismic Acoustics in Porous Soil: Thermoviscoelastic Equations and Lamé Equations

We consider a linear system of differential equations that describes the joint motion of an incompressible elastic porous body and an incompressible fluid filling the pores. The model is very complicated because the main differential equations contain the derivatives of expressions with nondifferentiable rapidly oscillating small and large coefficients. On the basis of Nguetseng's two-scale convergence method, we derive homogenized equations in a rigorous way; depending on the geometry of pores, these are either the thermoviscoelasticity equations (for a connected porous space) or the anisotropic thermoelastic Lamé system.