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Fibre Homogenisation

Cooper, Shane; Waurick, Marcus

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Authors

Shane Cooper

Marcus Waurick



Abstract

In this article we present a novel method for studying the asymptotic behaviour, with order-sharp error estimates, of the resolvents of parameter-dependent operator families. The method is applied to the study of differential equations with rapidly oscillating coefficients in the context of second-order PDE systems and the Maxwell system. This produces a non-standard homogenisation result that is characterised by ‘fibre-wise’ homogenisation of the related Floquet-Bloch PDEs. These fibre-homogenised resolvents are shown to be asymptotically equivalent to a whole class of operator families, including those obtained by standard homogenisation methods.

Citation

Cooper, S., & Waurick, M. (2019). Fibre Homogenisation. Journal of Functional Analysis, 276(11), 3363-3405. https://doi.org/10.1016/j.jfa.2019.03.004

Journal Article Type Article
Acceptance Date Mar 8, 2019
Online Publication Date Mar 21, 2019
Publication Date Jun 30, 2019
Deposit Date Mar 22, 2019
Publicly Available Date Mar 21, 2020
Journal Journal of Functional Analysis
Print ISSN 0022-1236
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 276
Issue 11
Pages 3363-3405
DOI https://doi.org/10.1016/j.jfa.2019.03.004

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