Fibre Homogenisation

Cooper, Shane and Waurick, Marcus (2017) Fibre Homogenisation. Preprint / Working Paper. arXiv.org, Ithaca, NY.

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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.

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• Item metadata

  Item type:	Monograph(Preprint / Working Paper)
  ID code:	61452
  Dates:	Date Event 2 June 2017 Published
  Subjects:	Science > Mathematics
  Department:	Faculty of Science > Mathematics and Statistics
  Depositing user:	Pure Administrator
  Date deposited:	03 Aug 2017 11:24
  Last modified:	09 Apr 2024 04:41
  Related URLs:	Publisher
  URI:	https://strathprints.strath.ac.uk/id/eprint/61452