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Trudy Moskovskogo Matematicheskogo Obshchestva
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Trudy Moskovskogo Matematicheskogo Obshchestva, 2019, Volume 80, Issue 2, Pages 295–342 (Mi mmo632)  
This article is cited in 5 scientific papers (total in 5 papers)

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
Full-text PDF (529 kB) Citations (5)
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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).
Received: 15.07.2019
English version:
Transactions of the Moscow Mathematical Society, 2019, Volume 80, Pages 251–294
DOI: https://doi.org/10.1090/mosc/291
Bibliographic databases:
Document Type: Article
UDC: 517.98
MSC: Primary 34E13; Secondary 34E05, 35P20, 47A20, 81Q35
Language: English
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}
\elib{https://elibrary.ru/item.asp?id=43256690}
\transl
\jour Trans. Moscow Math. Soc.
\yr 2019
\vol 80
\pages 251--294
\crossref{https://doi.org/10.1090/mosc/291}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85080920708}
Linking options:
  • https://www.mathnet.ru/eng/mmo632
  • https://www.mathnet.ru/eng/mmo/v80/i2/p295
    • This publication is cited in the following 5 articles:
    1. Florian Feppon, Habib Ammari, “Homogenization of sound-soft and high-contrast acoustic metamaterials in subcritical regimes”, ESAIM: M2AN, 57:2 (2023), 491  crossref
    2. V. A. Sloushch, T. A. Suslina, “Operator estimates for homogenization of higher-order elliptic operators with periodic coefficients”, St. Petersburg Math. J., 35:2 (2024), 327–375  mathnet  crossref
    3. A. V. Kiselev, L. O. Silva, K. D. Cherednichenko, “Operator-Norm Resolvent Asymptotic Analysis of Continuous Media with High-Contrast Inclusions”, Math. Notes, 111:3 (2022), 373–387  mathnet  crossref  crossref  mathscinet
    4. K. D. Cherednichenko, A. V. Kiselev, L. O. Silva, “Functional model for boundary-value problems”, Mathematika, 67:3 (2021), 596–626  crossref  mathscinet  isi  scopus
    5. K. D. Cherednichenko, Yu. Yu. Ershova, A. V. Kiselev, “Effective behaviour of critical-contrast pdes: micro-resonances, frequency conversion, and time dispersive properties. I”, Commun. Math. Phys., 375:3 (2020), 1833–1884  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Moskovskogo Matematicheskogo Obshchestva
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