The band-gap structure of the spectrum in a periodic medium of masonry type

Leugering G, Nazarov SA, Taskinen J (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Networks and Heterogeneous Media

Book Volume: 15

Pages Range: 555-580

Journal Issue: 4

DOI: 10.3934/nhm.2020014

Abstract

We consider the spectrum of a class of positive, second-order elliptic systems of partial differential equations defined in the plane R² . The coefficients of the equation are assumed to have a special form, namely, they are doubly periodic and of high contrast. More precisely, the plane R² is decomposed into an infinite union of the translates of the rectangular periodicity cell Ω⁰, and this in turn is divided into two components, on each of which the coefficients have different, constant values. Moreover, the second component of Ω⁰ consist of a neighborhood of the boundary of the cell of the width h and thus has an area comparable to h, where h > 0 is a small parameter. Using the methods of asymptotic analysis we study the position of the spectral bands as h → 0 and in particular show that the spectrum has at least a given, arbitrarily large number of gaps, provided h is small enough.

Authors with CRIS profile

Günter Leugering Lehrstuhl für Angewandte Mathematik

Involved external institutions

Saint Petersburg State University (SPbU) / Санкт-Петербургский государственный университет (СПбГУ)

Russian Federation (RU) Helsingin yliopisto / University of Helsinki

Finland (FI)

How to cite

APA:

Leugering, G., Nazarov, S.A., & Taskinen, J. (2020). The band-gap structure of the spectrum in a periodic medium of masonry type. Networks and Heterogeneous Media, 15(4), 555-580. https://doi.org/10.3934/nhm.2020014

MLA:

Leugering, Günter, Sergei A. Nazarov, and Jari Taskinen. "The band-gap structure of the spectrum in a periodic medium of masonry type." Networks and Heterogeneous Media 15.4 (2020): 555-580.

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