Geodesic
Homogenizing the Viscoelasticity Problem with Long-Term Memory
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 441-454

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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
Mots-clés : Laplace transform. 
@article{MZM_2013_94_3_a10,
     author = {V. V. Shumilova},
     title = {Homogenizing the {Viscoelasticity} {Problem} with {Long-Term} {Memory}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {441--454},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a10/}
}
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V. V. Shumilova. Homogenizing the Viscoelasticity Problem with Long-Term Memory. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 441-454. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a10/