### Abstract

We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities &epsilon have a high degree of contrast between each other. We assume that the ratio between the permittivities of the components with low and high values of &epsilon is of the order η<sup>2</sup>, where η>0 is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the homogenization limit, as η 0, and derive the limit system of Maxwell equations in R<sup>3</sup>. Our results extend a number of conclusions of a paper by Zhikov [On gaps in the spectrum of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(5) (2004), 719-773] to the case of the full system of Maxwell equations.

Language | English |
---|---|

Pages | 475-500 |

Number of pages | 26 |

Journal | Mathematika |

Volume | 61 |

Issue number | 2 |

Early online date | 27 Feb 2015 |

DOIs | |

Status | Published - May 2015 |

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*Mathematika*,

*61*(2), 475-500. https://doi.org/10.1112/S0025579314000424

**Homogenization of the system of high-contrast Maxwell equations.** / Cherednichenko, Kirill; Cooper, Shane.

Research output: Contribution to journal › Article

*Mathematika*, vol. 61, no. 2, pp. 475-500. https://doi.org/10.1112/S0025579314000424

}

TY - JOUR

T1 - Homogenization of the system of high-contrast Maxwell equations

AU - Cherednichenko, Kirill

AU - Cooper, Shane

PY - 2015/5

Y1 - 2015/5

N2 - We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities &epsilon have a high degree of contrast between each other. We assume that the ratio between the permittivities of the components with low and high values of &epsilon is of the order η2, where η>0 is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the homogenization limit, as η 0, and derive the limit system of Maxwell equations in R3. Our results extend a number of conclusions of a paper by Zhikov [On gaps in the spectrum of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(5) (2004), 719-773] to the case of the full system of Maxwell equations.

AB - We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities &epsilon have a high degree of contrast between each other. We assume that the ratio between the permittivities of the components with low and high values of &epsilon is of the order η2, where η>0 is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the homogenization limit, as η 0, and derive the limit system of Maxwell equations in R3. Our results extend a number of conclusions of a paper by Zhikov [On gaps in the spectrum of some divergent elliptic operators with periodic coefficients. St. Petersburg Math. J. 16(5) (2004), 719-773] to the case of the full system of Maxwell equations.

UR - http://www.scopus.com/inward/record.url?scp=84929049144&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1112/S0025579314000424

U2 - 10.1112/S0025579314000424

DO - 10.1112/S0025579314000424

M3 - Article

VL - 61

SP - 475

EP - 500

JO - Mathematika

T2 - Mathematika

JF - Mathematika

SN - 0025-5793

IS - 2

ER -