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Non-local homogenised limits for composite media with highly anisotropic periodic fibres

Cherednichenko, Kirill, Smyshlyaev, V. P. and Zhikov, V. V. 2006. Non-local homogenised limits for composite media with highly anisotropic periodic fibres. Proceedings of the Royal Society of Edinburgh Section A Mathematics 136 (1) , pp. 87-114. 10.1017/S0308210500004455

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We consider a homogenization problem for highly anisotropic conducting fibres embedded into an isotropic matrix. For a ‘double porosity’-type scaling in the expression of high contrast between the conductivity along the fibres and the conductivities in the transverse directions, we prove the homogenization theorem and derive two-scale homogenized equations using a version of the method of two-scale convergence, supplemented in the case when the spectral parameter λ = 0 by a newly derived variant of high-contrast Poincaré-type inequality. Further elimination of the 'rapid' component from the two-scale limit equations results in a non-local (convolution-type integro-differential) equation for the slowly varying part in the matrix, with the non-local kernel explicitly related to the Green function on the fibre. The regularity of the solution to the non-local homogenized equation is proved.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: PDF uploaded in accordance with publisher's policy as of 28/07/14.
Publisher: Royal Society of Edinburgh
ISSN: 14737124
Date of First Compliant Deposit: 30 March 2016
Last Modified: 18 Oct 2017 09:23

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