Homogenization of nonstationary Maxwell system with constant magnetic permeability

M. A. Dorodnyi ; T. A. Suslina

Funkcionalʹnyj analiz i ego priloženiâ, Tome 55 (2021) no. 2, pp. 100-106

Résumé

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.