Fibre Homogenisation

Cooper, Shane; Waurick, Marcus

doi:10.1016/j.jfa.2019.03.004

Fibre Homogenisation

Cooper, Shane; Waurick, Marcus

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

Files

Accepted Journal Article (505 Kb)
PDF

Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
© 2019 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/