## Abstract

We consider the Maxwell equations for a composite material consisting of two phases and enjoying a periodical structure in the presence of a time-harmonic current source. We perform the two-scale homogenization taking into account both the interfacial layer thickness and the complex conductivity of the interfacial layer. We introduce a variational formulation of the differential system equipped with boundary and interfacial conditions. We show the unique solvability of the variational problem. Then, we analyze the low frequency case, high and very high frequency cases, with different strength of the interfacial currents. We find the macroscopic equations and determine the effective constant matrices such as the magnetic permeability, dielectric permittivity, and electric conductivity. The effective matrices depend strongly on the frequency of the current source; the dielectric permittivity and electric conductivity also depend on the strength of the interfacial currents.

Original language | English |
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Pages (from-to) | 3140-3162 |

Number of pages | 23 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 40 |

Issue number | 8 |

DOIs | |

Publication status | Published - 30 May 2017 |

## Keywords

- homogenization
- interfacial currents
- Maxwell equations
- two-scale convergence
- 2-SCALE CONVERGENCE
- TRACES
- DECOMPOSITION