Geodesic
Acoustics equations in elastic porous media
Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 98-110

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We study the acoustics equations in elastic porous media which had been obtained by the author by averaging the exact dimensionless equations that describe the joint motion of an elastic solid skeleton and a viscous fluid in the pores on the microscopic level. The small parameter of this model is the ratio $\varepsilon$ of the average pore size $l$ to the characteristic size $L$ of the physical region under consideration. The averaged equations (the limit regimes of the exact model as $\varepsilon$ tends to zero) depend on the dimensionless coefficients of the model, which either depend weakly on the small parameter, or are small or large as this parameter tends to zero. On assuming that the solid skeleton is periodic we analyze the particular form of acoustics equations for the simplest periodic structures.
Keywords: Stokes and Lamé equations, two-scale convergence, acoustics equations. 
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     author = {A. M. Meǐrmanov},
     title = {Acoustics equations in elastic porous media},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {98--110},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2010_13_2_a9/}
}
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A. M. Meǐrmanov. Acoustics equations in elastic porous media. Sibirskij žurnal industrialʹnoj matematiki, Tome 13 (2010) no. 2, pp. 98-110. http://geodesic.mathdoc.fr/item/SJIM_2010_13_2_a9/