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首页> 外文期刊>Siberian Mathematical Journal >Nguetseng’s two-scale convergence method for filtration and seismic acoustic problems in elastic porous media
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Nguetseng’s two-scale convergence method for filtration and seismic acoustic problems in elastic porous media

机译：恩格森的两尺度收敛方法，用于弹性多孔介质中的过滤和地震声学问题

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摘要

A linear system is considered of the differential equations describing a joint motion of an elastic porous body and a fluid occupying a porous space. The problem is linear but very hard to tackle since its main differential equations involve some (big and small) nonsmooth oscillatory coefficients. Rigorous justification under various conditions on the physical parameters is fulfilled for the homogenization procedures as the dimensionless size of pores vanishes, while the porous body is geometrically periodic. In result, we derive Biot’s equations of poroelasticity, the system consisting of the anisotropic Lamé equations for the solid component and the acoustic equations for the fluid component, the equations of viscoelasticity, or the decoupled system consisting of Darcy’s system of filtration or the acoustic equations for the fluid component (first approximation) and the anisotropic Lamé equations for the solid component (second approximation) depending on the ratios between the physical parameters. The proofs are based on Nguetseng’s two-scale convergence method of homogenization in periodic structures.
机译：考虑微分方程的线性系统，该微分方程描述了弹性多孔体和占据多孔空间的流体的联合运动。这个问题是线性的，但是很难解决，因为它的主要微分方程涉及一些（大和小的）非光滑的振荡系数。对于均匀化程序，由于孔的无量纲尺寸消失了，而多孔体在几何上是周期性的，因此在各种条件下对均质程序都进行了严格的论证。结果，我们导出了Biot的多孔弹性方程，由固体成分的各向异性Lamé方程和流体成分的声学方程组成的系统，粘弹性方程或由Darcy过滤系统或声学方程组成的解耦系统取决于物理参数之间的比率，流体成分（第一近似）和各向异性Lamé方程（固体近似）（第二近似）。证明是基于Nguetseng的周期性结构均质化的两尺度收敛方法。

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