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Some analogues of the double-porositymodels and the associated effect of micro-resonance

Cherednichenko, Kirill 2011. Some analogues of the double-porositymodels and the associated effect of micro-resonance. Journal of Mathematical Sciences 176 (6) , pp. 818-827. 10.1007/s10958-011-0438-z

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A non-uniformly elliptic periodic partial differential equation is considered that exhibits a version of the band-gap phenomenon in the limit as the period of oscillations ε tends to zero. This equation represents an analogue of the so-called double porosity models, which have been the subject of intensive study recently. The description of the limit (homogenized) operator as ε → 0 is given, and the structure of its spectrum is investigated. The existence of “sparsely localized ” modes in the spectrum of the associated operator in the whole space is discussed. Bibliography: 11 titles.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Subjects: Q Science > QA Mathematics
Additional Information: From the issue entitled 'This issue is a translation of Problemy Matematicheskogo Analiza (Problems in Mathematical Analysis), No. 58, June 2011. Editorial Board of PMA: N. Uraltseva (Main Editor), N. Ivochkina, A. Laptev, B. Makarov, V. Maz’ya, V. Osmolovskii, B. Plamenevskii, G. Rozenblyum, D. Yafaev. Translated into English and edited by Tamara Rozhkovskaya (, This issue is dedicated to Professor V. V. Zhikov on the occasion of his 70th birthday'
Publisher: Springer
ISSN: 1072-3374
Funders: EPSRC
Last Modified: 04 Nov 2017 23:43

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