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

Kirill Cherednichenko; Yulia Ershova; Alexander Kiselev

doi:10.1007/s00220-020-03696-2

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 journal › Article › peer-review

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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.

Original language	English
Pages (from-to)	1833-1884
Number of pages	52
Journal	Communications in Mathematical Physics
Volume	375
Issue number	3
Early online date	21 Feb 2020
DOIs	https://doi.org/10.1007/s00220-020-03696-2
Publication status	Published - 31 May 2020

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10.1007/s00220-020-03696-2Licence: CC BY

https://arxiv.org/abs/1808.03961

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials
Cherednichenko, K.
The Royal Society
1/02/17 → 31/01/19
Project: Research council
Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K.
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council

Kirill Cherednichenko
- K.Cherednichenkobath.acuk
Person: Research & Teaching

Cite this

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title = "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.",

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AU - Ershova, Yulia

AU - Kiselev, Alexander

PY - 2020/5/31

Y1 - 2020/5/31

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AB - 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.

U2 - 10.1007/s00220-020-03696-2

DO - 10.1007/s00220-020-03696-2

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JF - Communications in Mathematical Physics

SN - 0010-3616

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

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Projects

Newton Mobility Grant -: Homogenisation of Degenerate Equations and Scattering for New Materials

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

Profiles

Kirill Cherednichenko

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