Fibre homogenisation

Shane Cooper, Marcus Waurick

Research output: Contribution to journalArticle

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

Fingerprint

Resolvent
Homogenization
Fiber
Oscillating Coefficients
Homogenization Method
Maxwell System
Asymptotically equivalent
Operator
Error Estimates
Asymptotic Behavior
Differential equation
Dependent
Family
Standards
Context
Class

Keywords

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

Cite this

Cooper, Shane ; Waurick, Marcus. / Fibre homogenisation. In: Journal of Functional Analysis. 2019 ; Vol. 276, No. 11. pp. 3363-3405.
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Fibre homogenisation. / Cooper, Shane; Waurick, Marcus.

In: Journal of Functional Analysis, Vol. 276, No. 11, 01.06.2019, p. 3363-3405.

Research output: Contribution to journalArticle

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