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.
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