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November/December 2012 Homogenization of a coupled problem for sound propagation in porous media
François Alouges, Adeline Augier, Benjamin Graille, Benoît Merlet
Adv. Differential Equations 17(11/12): 1001-1030 (November/December 2012). DOI: 10.57262/ade/1355702937


In this paper we study the acoustic properties of a microstructured material such as glass, wool, or foam. In our model, the solid matrix is governed by linear elasticity and the surrounding fluid obeys the Stokes equations. The microstructure is assumed to be periodic at some small scale ${\varepsilon}$ and the viscosity coefficient of the fluid is assumed to be of order ${\varepsilon}^2$. We consider the time-harmonic regime forced by vibrations applied on a part of the boundary. We use the two-scale convergence theory to prove the convergence of the displacements to the solution of a homogeneous problem as the size of the microstructure shrinks to 0.


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François Alouges. Adeline Augier. Benjamin Graille. Benoît Merlet. "Homogenization of a coupled problem for sound propagation in porous media." Adv. Differential Equations 17 (11/12) 1001 - 1030, November/December 2012.


Published: November/December 2012
First available in Project Euclid: 17 December 2012

zbMATH: 1261.35014
MathSciNet: MR3013411
Digital Object Identifier: 10.57262/ade/1355702937

Primary: 35B27 , 74F10

Rights: Copyright © 2012 Khayyam Publishing, Inc.


Vol.17 • No. 11/12 • November/December 2012
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