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Journal Articles Annales Henri Lebesgue Year : 2019

Asymptotic expansions for the conductivity problem with nearly touching inclusions with corner

Abstract

We investigate the case of a medium with two inclusions or inhomogeneities with nearly touching corner singularities. We present two different asymptotic models to describe the phenomenon under specific geometrical assumptions. These asymptotic expansions are analysed and compared in a common framework. We conclude by a representation formula to characterise the detachment of the corners and we provide the possible extensions of the geometrical hypotheses.
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Dates and versions

hal-01766052 , version 1 (13-04-2018)
hal-01766052 , version 2 (28-06-2019)

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Virginie Bonnaillie-Noël, Clair Poignard, Grégory Vial. Asymptotic expansions for the conductivity problem with nearly touching inclusions with corner. Annales Henri Lebesgue, 2019, 3, pp.381-406. ⟨10.5802/ahl.36⟩. ⟨hal-01766052v2⟩
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