Effective Behaviour of Critical-Contrast PDEs: Micro-resonances, Frequency Conversion, and Time Dispersive Properties. I
Effective Behaviour of Critical-Contrast PDEs: Micro-resonances, Frequency Conversion, and Time Dispersive Properties. I
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DOI：
10.1007/s00220-020-03696-2
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发表时间：
2018-08
影响因子：
2.4
通讯作者：
K. Cherednichenko;Yulia Ershova;A. Kiselev
中科院分区：
文献类型：
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作者：
K. Cherednichenko;Yulia Ershova;A. Kiselev
通过对Dirichlet-to-Neumann算子的显式渐近分析，提出了周期偏微分方程临界对比均匀化的新方法。构造了具有高振荡系数的非一致椭圆型问题的范数解渐近性。新技术的一个基本特征是它将均质化限制与一类时间色散介质联系起来。
A novel approach to critical-contrast homogenisation for periodic PDEs is proposed, via an explicit asymptotic analysis of Dirichlet-to-Neumann operators. Norm-resolvent asymptotics for non-uniformly elliptic problems with highly oscillating coefficients are explicitly constructed. An essential feature of the new technique is that it relates homogenisation limits to a class of time-dispersive media.