Fibre homogenisation

Shane Cooper, Marcus Waurick

Research output: Contribution to journalArticle

1 Citation (Scopus)
1 Downloads (Pure)

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.

Original languageEnglish
Pages (from-to)3363-3405
Number of pages43
JournalJournal of Functional Analysis
Volume276
Issue number11
Early online date21 Mar 2019
DOIs
Publication statusPublished - 1 Jun 2019

Keywords

  • fibre homogenisation
  • Maxwell's equations
  • resolvent estimates
  • second-order PDE systems

Fingerprint Dive into the research topics of 'Fibre homogenisation'. Together they form a unique fingerprint.

  • Profiles

    Cite this