Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I

Abstract

A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotics for non-uniformly elliptic problems with highly oscillating coefficients are explicitly constructed. An essential feature of the new technique is that it relates homogenisation limits to a class of time-dispersive media.

arXiv comment40 pages, 1 figure

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Cited by in corpus (4)

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• Sharp operator-norm asymptotics for thin elastic plates with rapidly oscillating periodic properties
• Operator-norm resolvent asymptotic analysis of continuous media with high-contrast inclusions