Homogenization of spectral problems in bounded domains with doubly high contrasts

Homogenization of spectral problems in bounded domains with doubly high contrasts
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双倍高对比度有界域中光谱问题的均质化

DOI：
10.3934/nhm.2008.3.413
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发表时间：
2007
期刊：
Networks Heterog. Media
影响因子：
--
通讯作者：
V. Smyshlyaev
V. Smyshlyaev
中科院分区：
--
文献类型：
--
作者：
N. Babych;I. Kamotski;V. Smyshlyaev

文献摘要

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有界区域上一类谱问题的均匀化 考虑刚度和密度的对比度。为了某一个特别 临界标度，特征值的双标度渐近展开 并构造特征函数。双尺度极限方程为 导出并与某些非标准自伴算子相关。 特别地，它们显式地显示 渐近展开的特征值，一个令人惊讶的界限 对于阶数为$\vareps ^{5/4}$的错误，证明了。
Homogenization of a spectral problem in a bounded domain with a high contrast in both stiffness and density is considered. For a special critical scaling, two-scale asymptotic expansions for eigenvalues and eigenfunctions are constructed. Two-scale limit equations are derived and relate to certain non-standard self-adjoint operators. In particular they explicitly display the first two terms in the asymptotic expansion for the eigenvalues, with a surprising bound for the error of order $\varepsilon^{5/4}$ proved.