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arXiv · 1808.03961

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

Kirill Cherednichenko·Yulia Ershova·Alexander Kiselev
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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.

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Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev. 2018-08-12. Effective behaviour of critical-contrast PDEs: micro-resonances, frequency conversion, and time dispersive properties. I. https://doi.org/10.1007/s00220-020-03696-2

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