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

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

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4 Finished

Bath-Chile-Mexico Network
Kyprianou, A., Cherednichenko, K., Cox, A., Musso, M., Del Pino, M., Majumdar, A., Maas, A., Jara, A., Rivero, V. & Benítez, H.
1/07/18 → 31/08/20
Project: Research-related funding
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
Global Mobility Scheme - Metamaterials and scattering: Mathematical Foundations
Cherednichenko, K.
1/03/15 → 1/02/16
Project: Research-related funding

Kirill Cherednichenko
- K.Cherednichenko@bath.ac.uk
- Department of Mathematical Sciences - Reader
- EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
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 - 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.

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JF - Communications in Mathematical Physics

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

Abstract

Access to Document

Bath-Chile-Mexico Network

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

Global Mobility Scheme - Metamaterials and scattering: Mathematical Foundations

Kirill Cherednichenko

Cite this