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

Kirill Cherednichenko, Yulia Ershova, Alexander Kiselev

Research output: Contribution to journalArticle

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.
Original languageEnglish
Pages (from-to)1833-1884
Number of pages52
JournalCommunications in Mathematical Physics
Volume375
Issue number3
Early online date21 Feb 2020
DOIs
Publication statusPublished - 1 May 2020

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