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Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations

 

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Opened Access Homogenization of stiff plates and two-dimensional high-viscosity Stokes equations
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Author: Briane, Marc
Casado Díaz, Juan
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2012-09
Published in: Archive for Rational Mechanics and Analysis, 205 (3), 753-794.
Document type: Article
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 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.
Cite: 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.
Size: 423.0Kb
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URI: http://hdl.handle.net/11441/46225

DOI: 10.1007/s00205-012-0520-9

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