Homogenization of the spectral Dirichlet problem for a system of differential equations with rapidly oscillating coefficients and changing sign density

被引：0

作者：

Nazarov S.A. ^{[1
]}

Pyatnitskii A.L. ^{[2
,3
]}

机构：

[1] Institute of Problems in Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg 199178, 61, Bolshoi pr. V.O.

[2] The Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119333, 53, Leninskiy pr.

[3] Narvik Institute of Technology

来源：

Journal of Mathematical Sciences | 2010年 / 169卷 / 2期

关键词：

Discrete Spectrum; Spectral Problem; Periodicity Cell; Integral Identity; Simple Eigenvalue;

D O I：

10.1007/s10958-010-0047-2

中图分类号：

学科分类号：

摘要：

We study the asymptotic behavior of the spectrum of the Dirichlet problem for a formally selfadjoint elliptic system of differential equations with rapidly oscillating coefficients and changing sign density ρ. Since the factor ρ at the spectral parameter changes sign, the problem possesses two - positive and negative - infinitely large sequences of eigenvalues. Their asymptotic structure essentially depends on whether the mean ρ̄ over the periodicity cell vanishes. In particular, in the case ρ̄ = 0, the homogenized problem becomes a quadratic pencil. Bibliography: 20 titles. © 2010 Springer Science+Business Media, Inc.

引用

页码：212 / 248

页数：36

共 19 条

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