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July  2008, 10(1): 91-107. doi: 10.3934/dcdsb.2008.10.91

Homogenization of the Maxwell's system for conducting media

Jiann-Sheng Jiang 1, , Chi-Kun Lin 2, and  Chi-Hua Liu 3,

1. 

Department of Electronics Engineering and Computer Science, Tung Fang Institute of Technology, Kaohsiung 829, Taiwan
2. 

Department of Applied Mathematics, National Chiao Tung University, Hsinchu 30010, Taiwan
3. 

General Education Center, Fortune Institute of Technology, Kaohsiung, Taiwan

Received  February 2007 Revised  October 2007 Published  April 2008

This paper is devoted to the study of the memory effect induced by homogenization of the Maxwell system for conducting media. The memory kernel is described by the Volterra integral equation. Furthermore, it can be characterized explicitly in terms of Young’s measure, and the kinetic formulation of the homogenized equation is also obtained. The kinetic formulation allows us to obtain the homogenization of the energy density and the associated conservation law with the Poynting vector. The interesting interaction phenomenon of the microscopic and macroscopic scales is also discussed and the memory effect explains qualitatively something about irreversibility.
Keywords: conducting media, Homogenization, Young's measure, Volterra integral equation, Maxwell equation, kinetic formulation., weak limit, memory (nonlocal) effect.
Mathematics Subject Classification: 35B27, 35B35, 74Q10, 76M5.
Citation: Jiann-Sheng Jiang, Chi-Kun Lin, Chi-Hua Liu. Homogenization of the Maxwell's system for conducting media. Discrete and Continuous Dynamical Systems - B, 2008, 10 (1) : 91-107. doi: 10.3934/dcdsb.2008.10.91
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