Effective Behaviour of Critical-Contrast PDEs: Micro-resonances, Frequency Conversion, and Time Dispersive Properties. I
Kirill D. Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev
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Source: Crossref
Published: Feb 21, 2020
DOI: 10.1007/s00220-020-03696-2
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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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