Effects of Rayleigh Waves on the Essential Spectrum in Perturbed Doubly Periodic Elliptic Problems

被引：8

作者：

Bakharev, F. L. ^{[1
]}

Cardone, G. ^{[2
]}

Nazarov, S. A. ^{[3
,4
,5
]}

Taskinen, J. ^{[6
]}

机构：

[1] St Petersburg State Univ, Math & Mech Fac, 7-9 Univ Nab, St Petersburg 199034, Russia

[2] Univ Sannio, Dept Engn, Corso Garibaldi 107, I-82100 Benevento, Italy

[3] St Petersburg State Univ, Univ Sky Pr 28, Stary Peterhof 198504, Russia

[4] Peter Great St Petersburg State Polytech Univ, Polytechn Skaya Ul 29, St Petersburg 195251, Russia

[5] RAS, Inst Problems Mech Engn, VO Bolshoj Pr 61, St Petersburg 199178, Russia

[6] Univ Helsinki, Dept Math & Stat, POB 68, Helsinki 00014, Finland

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2017年 / 88卷 / 03期

基金：

芬兰科学院;

关键词：

Periodic media; Open waveguides; High contrast of coefficients; Asymptotics; Spectral bands; DIFFERENTIAL-EQUATIONS; RADIATION CONDITIONS; GUIDES; MEDIA;

D O I：

10.1007/s00020-017-2379-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give an example of a scalar second order differential operator in the plane with double periodic coefficients and describe its modification, which causes an additional spectral band in the essential spectrum. The modified operator is obtained by applying to the coefficients a mirror reflection with respect to a vertical or horizontal line. This change gives rise to Rayleigh type waves localized near the line. The results are proven using asymptotic analysis, and they are based on high contrast of the coefficient functions.

引用

页码：373 / 386

页数：14

共 18 条

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F. L. Bakharev
G. Cardone
S. A. Nazarov
J. Taskinen
Integral Equations and Operator Theory, 2017, 88 : 373 - 386
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SCHECHTE.M
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Differential Equations, 2022, 58 : 631 - 648
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DIFFERENTIAL EQUATIONS, 2022, 58 (05) : 631 - 648
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Suzuki, Akito
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[9] Gap in the essential spectrum of the Neumann problem for an elliptic system in a periodic domain
S. A. Nazarov
Functional Analysis and Its Applications, 2009, 43 : 239 - 241
[10] Gap in the essential spectrum of the Neumann problem for an elliptic system in a periodic domain
Nazarov, S. A.
FUNCTIONAL ANALYSIS AND ITS APPLICATIONS, 2009, 43 (03) : 239 - 241

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