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.
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To Vasily Vasilievich Zhikov on his 70th birthday
Translated from Problems in Mathematical Analysis 58, June 2011, pp. 99–106.
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Cherednichenko, K.D. Some analogues of the double-porositymodels and the associated effect of micro-resonance. J Math Sci 176, 818–827 (2011). https://doi.org/10.1007/s10958-011-0438-z
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DOI: https://doi.org/10.1007/s10958-011-0438-z