Cooper, Shane and Waurick, Marcus (2019) 'Fibre homogenisation.', Journal of functional analysis., 276 (11). pp. 3363-3405.
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.
| Item Type: | Article |
|---|---|
| Full text: | (AM) Accepted Manuscript Available under License - Creative Commons Attribution Non-commercial No Derivatives. Download PDF (493Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1016/j.jfa.2019.03.004 |
| Publisher 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/ |
| Date accepted: | 08 March 2019 |
| Date deposited: | 22 March 2019 |
| Date of first online publication: | 21 March 2019 |
| Date first made open access: | 21 March 2020 |
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