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Homogenizing the viscoelasticity problem with long-term memory

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Abstract

The system of integro-differential equations describing the small oscillations of an ɛ-periodic viscoelastic material with long-term memory is considered. Using the two-scale convergencemethod, we construct the systemof homogenized equations and prove the strong convergence as ɛ → 0 of the solutions of prelimit problems to the solution of the homogenized problem in the norm of the space L 2.

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Authors and Affiliations

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

    V. V. Shumilova

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  1. V. V. Shumilova
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Correspondence to V. V. Shumilova.

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Original Russian Text © V. V. Shumilova, 2013, published in Matematicheskie Zametki, 2013, Vol. 94, No. 3, pp. 441–454.

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Shumilova, V.V. Homogenizing the viscoelasticity problem with long-term memory. Math Notes 94, 414–425 (2013). https://doi.org/10.1134/S0001434613090125

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