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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2012

Homogenization of Stiff Plates and Two-Dimensional High-Viscosity Stokes Equations

Résumé

The paper deals with the homogenization of stiff heterogeneous plates. Assuming that the coefficients are equi-bounded in L (1), we prove that the limit of a sequence of plate equations remains a plate equation which involves a strongly local linear operator acting on the second gradients. This compactness result is based on a div-curl lemma for fourth-order equations. On the other hand, using an intermediate stream function we deduce from the plates case a similar result for high-viscosity Stokes equations in dimension two, so that the nature of the Stokes equation is preserved in the homogenization process. Finally, we show that the L (1)-boundedness assumption cannot be relaxed. Indeed, in the case of the Stokes equation the concentration of one very rigid strip on a line induces the appearance of second gradient terms in the limit problem, which violates the compactness result obtained under the L (1)-boundedness condition.
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Dates et versions

hal-00736565 , version 1 (03-07-2013)

Identifiants

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Marc Briane, Juan Casado-Diaz. Homogenization of Stiff Plates and Two-Dimensional High-Viscosity Stokes Equations. Archive for Rational Mechanics and Analysis, 2012, 205 (3), pp.753-794. ⟨10.1007/s00205-012-0520-9⟩. ⟨hal-00736565⟩
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