On gaps in the spectrum of the operator of elasticity theory on a high contrast periodic structure
On gaps in the spectrum of the operator of elasticity theory on a high contrast periodic structure
复制标题
高对比度周期结构弹性理论算子谱中的间隙
DOI：
10.1007/s10958-012-1121-8
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发表时间：
2013
影响因子：
--
通讯作者：
S. Pastukhova
中科院分区：
文献类型：
--
作者：
V. Zhikov;S. Pastukhova
本文研究弹性力学中一个周期问题的谱，使得方程的系数对小参数ε具有高对比度。我们证明了当ε足够小时，连续谱中存在间断，间断的数目无限地增加，并且谱的极限集可以被精确地描述.证明是基于弹性模量的硬相和软相之间的对比系数为1：ε2的ε-周期两相弹性介质的双尺度平均原理。参考书目：11种。
We study the spectrum of a periodic problem of elasticity theory such that the coefficients of the equation are high contrast dependent on a small parameter ε. We prove that for sufficiently small ε there are gaps in the continuous spectrum, the number of gaps unboundedly increases, and the limit set for the spectrum can be exactly described. The proof is based on the two-scale averaging principle for an ε-periodic two-phase elastic medium with the contrast coefficient 1 : ε2 between hard and soft phases in moduli of elasticity. Bibliography: 11 titles.