Acoustic and filtration properties of a thermoelastic porous medium: Biot's equations of thermo-poroelasticity
Anvarbek Mukatovich Meirmanov · Sbornik Mathematics · 2008
Abstract. A linear system of differential equations describing a joint motion of thermoelastic porous body and incompressible thermofluid occupying 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 oscillatory coefficients, both big and small, under the differentiation operators. The rigorous justification is fulfilled for homogenization procedures as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic. As the results, we derive Biot’s like system of equations of thermo-poroelasticity, system of equations of thermo-viscoelasticity, or system of non-isotropic Lamé’s equations depending on ratios between physical parameters and geometry of porous space. The proofs are based on Nguetseng’s two-scale convergence method of homogenization in periodic structures. Key words: Biot’s equations, Stokes equations, Lamé’s equations, two-scale convergence, homogenization of periodic structures, thermo-poroelasticity.