Article
Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
Author/s | Briane, Marc
Casado Díaz, Juan |
Department | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Publication Date | 2012-09 |
Deposit Date | 2016-09-28 |
Published in |
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Abstract | The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, we prove that the limit of a sequence of plate equations remains a plate equation which involves ... The paper deals with the homogenization of rigid heterogeneous plates. Assuming that the coefficients are equi-bounded in L1, 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 fourthorder 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 L1-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 L1-boundedness condition. |
Funding agencies | Ministerio de Economía y Competitividad (MINECO). España |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2011-24457 |
Citation | Briane, M. y Casado Díaz, J. (2012). Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations. Archive for Rational Mechanics and Analysis, 205 (3), 753-794. |
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