Fibre Homogenisation

Shane Cooper, Marcus Waurick

Research output: Working paper

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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
Place of PublicationIthaca, NY
Number of pages38
Publication statusPublished - 2 Jun 2017

Keywords

  • resolvent estimates
  • fibre homogenisation
  • Gelfand transform
  • oscillating co-efficients

Cite this

Cooper, S., & Waurick, M. (2017). Fibre Homogenisation. Ithaca, NY.