Fibre homogenisation

Cooper, Shane and Waurick, Marcus (2019) Fibre homogenisation. Journal of Functional Analysis, 276 (11). pp. 3363-3405. ISSN 0022-1236

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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.