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Tr. Mosk. Mat. Obs., 2019, Volume 80, Issue 2, Pages 295–342 (Mi mmo632)  

Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media

K. D. Cherednichenkoa, Yu. Yu. Ershovaab, A. V. Kiselevcd, S. N. Nabokoef

a Department of Mathematical Sciences, University of Bath, United Kingdom
b Department of Mathematics, St. Petersburg State University of Architecture and Civil Engineering, Russia
c International research laboratory Multiscale Model Reduction, Ammosov North-Eastern Federal University, Yakutsk, Russia
d Departamento de Física Matemática, Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México
e Department of Higher Mathematics and Mathematical Physics, St. Petersburg State University, Russia
f Department of Mathematics, Stockholm University, Sweden

Abstract: A novel approach to critical-contrast homogenisation is proposed. Norm-resolvent asymptotics are explicitly constructed. An essential feature of our approach is that it relates homogenisation limits to a class of time-dispersive media.

Key words and phrases: Homogenisation, critical-contrast, time dispersion, graphs, dilation, generalised resolvent.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00657_a
Knut and Alice Wallenbergs Foundation
Ministry of Education and Science of the Russian Federation 14.Y26.31.0013
Engineering and Physical Sciences Research Council EP/L018802/2
The first and second authors are grateful for the financial support of the Engineering and Physical Sciences Research Council: Grant EP/L018802/2 “Mathematical foundations of metamaterials: homogenisation, dissipation and operator theory”.
The second and fourth authors were supported in part by the RFBR grant 19-01-00657-a.
The third author was supported in part by the Russian Federation Government megagrant 14.Y26.31.0013.
The fourth author also gratefully acknowledges funding provided by the Knut and Alice Wallenberg Foundation (program for mathematics 2018).


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English version:
Transactions of the Moscow Mathematical Society, 2019, 80, 251–294

UDC: 517.98
MSC: Primary 34E13; Secondary 34E05, 35P20, 47A20, 81Q35
Received: 15.07.2019
Language:

Citation: K. D. Cherednichenko, Yu. Yu. Ershova, A. V. Kiselev, S. N. Naboko, “Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media”, Tr. Mosk. Mat. Obs., 80, no. 2, MCCME, M., 2019, 295–342; Trans. Moscow Math. Soc., 80 (2019), 251–294

Citation in format AMSBIB
\Bibitem{CheErsKis19}
\by K.~D.~Cherednichenko, Yu.~Yu.~Ershova, A.~V.~Kiselev, S.~N.~Naboko
\paper Unified approach to critical-contrast homogenisation with explicit links to time-dispersive media
\serial Tr. Mosk. Mat. Obs.
\yr 2019
\vol 80
\issue 2
\pages 295--342
\publ MCCME
\publaddr M.
\mathnet{http://mi.mathnet.ru/mmo632}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 251--294
\crossref{https://doi.org/10.1090/mosc/291}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85080920708}


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