Non-local homogenized limits for composite media with highly anisotropic periodic fibres
Non-local homogenized limits for composite media with highly anisotropic periodic fibres
复制标题
具有高度各向异性周期性纤维的复合介质的非局部均匀化极限
DOI：
10.1017/s0308210500004455
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
V. Zhikov
中科院分区：
文献类型：
--
作者：
K. Cherednichenko;V. Smyshlyaev;V. Zhikov
我们考虑一个均匀化问题的高度各向异性导电纤维嵌入到各向同性矩阵。对于“双孔隙”型标度，在表示沿纤维沿着方向的电导率和横向电导率之间的高对比度时，我们证明了均匀化定理，并使用双尺度收敛方法的一个版本导出了双尺度均匀化方程，在谱参数λ = 0的情况下，补充了一个新导出的高对比度Poincaré型不等式的变体。进一步消除的“快速”组件从两个规模的极限方程的结果在一个非本地（卷积型积分微分）方程的缓慢变化的部分在矩阵中，与非本地内核明确相关的纤维上的绿色函数。证明了非局部齐次方程解的正则性。
We consider a homogenization problem for highly anisotropic conducting fibres embedded into an isotropic matrix. For a ‘double porosity’-type scaling in the expression of high contrast between the conductivity along the fibres and the conductivities in the transverse directions, we prove the homogenization theorem and derive two-scale homogenized equations using a version of the method of two-scale convergence, supplemented in the case when the spectral parameter λ = 0 by a newly derived variant of high-contrast Poincaré-type inequality. Further elimination of the 'rapid' component from the two-scale limit equations results in a non-local (convolution-type integro-differential) equation for the slowly varying part in the matrix, with the non-local kernel explicitly related to the Green function on the fibre. The regularity of the solution to the non-local homogenized equation is proved.