Abstract

We study a nonstationary Maxwell system in \(\mathbb{R}^3\) with dielectric permittivity \(\eta(\varepsilon^{-1}{\mathbf x})\) and magnetic permeability \(\mu\). Here \(\eta(\mathbf{x})\) is a positive definite bounded symmetric \((3 \times 3)\)-matrix- valued function periodic with respect to some lattice and \(\mu\) is a constant positive \(3\times 3\) matrix. We obtain approximations for the solutions in the \(L_2(\mathbb{R}^3;\mathbb{C}^3)\)-norm for a fixed time with error estimates of operator type.

中文翻译：

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具有恒定磁导率的非平稳麦克斯韦系统的均质化

摘要

我们研究了\(\mathbb{R}^3\) 中的非平稳麦克斯韦系统，其介电常数为\(\eta(\varepsilon^{-1}{\mathbf x})\)和磁导率\(\mu\) . 这里\(\eta(\mathbf{x})\)是一个正定有界对称\((3 \times 3)\) -矩阵值函数，相对于某个格子是周期性的，\(\mu\)是一个常数正\(3\times 3\)矩阵。我们在固定时间内获得\(L_2(\mathbb{R}^3;\mathbb{C}^3)\) -norm 中解的近似值，并使用运算符类型的误差估计。