热弹性多孔介质的声学与过滤特性：热孔隙弹性理论的Biot方程
Acoustic and Filtration Properties of Thermo-elastic porous medium: Biot's Equations of Thermo- Poroelasticity
AI总结：
本文针对含热流体的周期性热弹性多孔介质，采用Nguetseng两尺度收敛方法完成均匀化论证，推导得到不同形式的类Biot热孔隙弹性等方程组，解决了含振荡系数线性微分系统的处理难题。
摘要：
本文研究描述热弹性多孔体与占据其孔隙空间的不可压缩热流体联合运动的线性微分方程组。尽管该问题是线性的，但由于其主微分方程在求导算子下包含非光滑振荡系数（包括大系数与小系数），因此极难处理。当孔隙的无量纲尺寸趋于零且多孔体具有几何周期性时，本文完成了 homogenization（均匀化）过程的严格论证。作为结果，根据物理参数与孔隙空间几何结构的比值，本文推导得到类Biot的热孔隙弹性方程组、热粘弹性方程组或非各向同性Lamé方程组。证明基于Nguetseng提出的周期结构均匀化的两尺度收敛方法。
英文摘要：
A linear system of differential equations describing a joint motion of thermo-elastic porous body and incompressible thermo-fluid 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
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