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

Standard

The band-gap structure of the spectrum in a periodic medium of masonry type. / Leugering, Günter; Nazarov, Sergei A.; Taskinen, Jari.

In: Networks and Heterogeneous Media, Vol. 15, No. 4, 12.2020, p. 555-580.

Research output: Contribution to journal › Article › peer-review

Author

Leugering, Günter ; Nazarov, Sergei A. ; Taskinen, Jari. / The band-gap structure of the spectrum in a periodic medium of masonry type. In: Networks and Heterogeneous Media. 2020 ; Vol. 15, No. 4. pp. 555-580.

BibTeX

@article{87eacb2bfff04986b34dd45b7a1534cf,

title = "The band-gap structure of the spectrum in a periodic medium of masonry type",

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.",

keywords = "Band-gap spectrum, Essential spectrum, Periodic medium, Second order elliptic system, Spectral gap, periodic medium, band-gap spectrum, essential spectrum, spectral gap",

author = "G{\"u}nter Leugering and Nazarov, {Sergei A.} and Jari Taskinen",

note = "Funding Information: 2020 Mathematics Subject Classification. Primary: 35J57; Secondary: 35P99, 47B25. Key words and phrases. Second order elliptic system, essential spectrum, periodic medium, band-gap spectrum, spectral gap. The second named author was supported by the Russian Foundation on Basic Research, project 18-01-00325. Publisher Copyright: {\textcopyright} American Institute of Mathematical Sciences. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = dec,

doi = "10.3934/nhm.2020014",

language = "English",

volume = "15",

pages = "555--580",

journal = "Networks and Heterogeneous Media",

issn = "1556-1801",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

RIS

TY - JOUR

T1 - The band-gap structure of the spectrum in a periodic medium of masonry type

AU - Leugering, Günter

AU - Nazarov, Sergei A.

AU - Taskinen, Jari

N1 - Funding Information: 2020 Mathematics Subject Classification. Primary: 35J57; Secondary: 35P99, 47B25. Key words and phrases. Second order elliptic system, essential spectrum, periodic medium, band-gap spectrum, spectral gap. The second named author was supported by the Russian Foundation on Basic Research, project 18-01-00325. Publisher Copyright: © American Institute of Mathematical Sciences. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Band-gap spectrum

KW - Essential spectrum

KW - Periodic medium

KW - Second order elliptic system

KW - Spectral gap

KW - periodic medium

KW - band-gap spectrum

KW - essential spectrum

KW - spectral gap

UR - http://www.scopus.com/inward/record.url?scp=85095864054&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/abf3f760-7c56-3b3c-b843-a9c3a84234dc/

U2 - 10.3934/nhm.2020014

DO - 10.3934/nhm.2020014

M3 - Article

AN - SCOPUS:85095864054

VL - 15

SP - 555

EP - 580

JO - Networks and Heterogeneous Media

JF - Networks and Heterogeneous Media

SN - 1556-1801

IS - 4

ER -

ID: 71561948