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Mat. Zametki, 2013, Volume 94, Issue 3, Pages 441–454 (Mi mz8897)  

Homogenizing the Viscoelasticity Problem with Long-Term Memory

V. V. Shumilova

A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences, Moscow

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

Keywords: viscoelasticity problem with long-term memory, homogenized viscoelasticity problem, system of integro-differential equations, two-scale convergence method, Galerkin method, Laplace transform.

DOI: https://doi.org/10.4213/mzm8897

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English version:
Mathematical Notes, 2013, 94:3, 414–425

Bibliographic databases:

UDC: 517.958
Received: 19.05.2011
Revised: 16.01.2013

Citation: V. V. Shumilova, “Homogenizing the Viscoelasticity Problem with Long-Term Memory”, Mat. Zametki, 94:3 (2013), 441–454; Math. Notes, 94:3 (2013), 414–425

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