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Lower and upper bounds for the Rayleigh conductivity of a perforated plate

S. LaurensS. TordeuxA. BendaliM. FaresP. R. Kotiuga — 2013

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Lower and upper bounds for the Rayleigh conductivity of a perforation in a thick plate are usually derived from intuitive approximations and by physical reasoning. This paper addresses a mathematical justification of these approaches. As a byproduct of the rigorous handling of these issues, some improvements to previous bounds for axisymmetric holes are given as well as new estimates for tilted perforations. The main techniques are a proper use of the Dirichlet and Kelvin variational principlesin...

Multiscale expansion and numerical approximation for surface defects ⋆

V. Bonnaillie-NoëlD. BrancherieM. DambrineF. HérauS. TordeuxG. Vial — 2011

ESAIM: Proceedings

This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...

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