HOMOGENIZATION OF THE SYSTEM OF HIGH-CONTRAST MAXWELL EQUATIONS. Issue 2 (27th February 2015)

• Record Type: Journal Article
• Authors: Cherednichenko, Kirill; Cooper, Shane
• Is Part Of: Mathematika. Volume 61:Issue 2(2015)
• Page Start: 475
• Page End: 500
• Publication Date: 2015-02-27
• Subjects: 35J15, -- 35J70, -- 47F05 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579314000424
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract : We study the system of Maxwell equations for a periodic composite dielectric medium with components whose dielectric permittivities ${\it\epsilon}$ 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 ${\it\epsilon}$ is of the order ${\it\eta}^{2}$, where ${\it\eta}>0$ is the period of the medium. We determine the asymptotic behaviour of the electromagnetic response of such a medium in the "homogenization limit", as ${\it\eta}\rightarrow 0$, and derive the limit system of Maxwell equations in $\mathbb{R}^{3}$ . 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.