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.
|Place of Publication||Ithaca, NY|
|Number of pages||38|
|Publication status||Published - 2 Jun 2017|
- resolvent estimates
- fibre homogenisation
- Gelfand transform
- oscillating co-efficients