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Homogenization of the acoustic equations for a porous long-memory viscoelastic material filled with a viscous fluid

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Abstract

We consider the system of linear differential and integro-differential equations describing small vibrations in an ɛ-periodic combined medium consisting of a porous long-memory viscoelastic material and a viscous fluid filling the pores. By using the two-scale convergence method, we construct the system of homogenized equations and prove the convergence of solutions of the original problems to the solution of the homogenized problem as ɛ → 0.

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Authors and Affiliations

  1. Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, Russia

    A. S. Shamaev & V. V. Shumilova

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  1. A. S. Shamaev
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  2. V. V. Shumilova
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Original Russian Text © A.S. Shamaev, V.V. Shumilova, 2012, published in Differentsial’nye Uravneniya, 2012, Vol. 48, No. 8, pp. 1174–1186.

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Shamaev, A.S., Shumilova, V.V. Homogenization of the acoustic equations for a porous long-memory viscoelastic material filled with a viscous fluid. Diff Equat 48, 1161–1173 (2012). https://doi.org/10.1134/S0012266112080113

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  • DOI: https://doi.org/10.1134/S0012266112080113

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