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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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Abstract

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 (rozhk@mathbooks.ru, rozhk@math.nsc.ru). 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
URI: http://orca.cf.ac.uk/id/eprint/13408

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