热弹性多孔介质中的均质化、过滤与地震声学问题
Homogenization and Filtration and Seismic Acoustic Problems in Thermo-elastic Porous Media
AI总结：
本文针对热弹性多孔介质的线性耦合运动问题，采用Nguetseng的两尺度收敛方法，在孔隙尺寸趋于零的周期结构下严格论证均质化过程，推导得到三类不同的热相关耦合或解耦方程组。
摘要：
本文研究了描述热弹性多孔体与占据其孔隙空间的热流体共同运动的线性微分方程组。尽管该问题是线性的，但因主微分算子下包含大小不一的非光滑振荡系数而极难处理。当孔隙的无量纲尺寸趋于零且多孔体为几何周期结构时，本文在对物理参数施加各类条件下严格论证了均质化过程。结果表明，依据物理参数的比值，可推导出类似Biot的热孔隙弹性方程组、热粘弹性方程组，或由热弹性固体的非各向同性Lamé方程与热流体过滤的Darcy方程组组成的解耦系统。证明基于Nguetseng提出的周期结构均质化两尺度收敛方法。
英文摘要：
A linear system of differential equations describing a joint motion of thermoelastic porous body and 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, under various conditions imposed on physical parameters, 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 decoupled system consisting of non-isotropic Lamé's equations for thermoelastic solid and Darcy's system of filtration for thermofluid, depending on ratios between physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.
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