中国物理B ›› 2007, Vol. 16 ›› Issue (9): 2523-2536.doi: 10.1088/1009-1963/16/9/006

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Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

谢莉, 雷银照   

  1. Department of Electrical Engineering, School of Automation and Electrical Engineering, \ Beihang University, Beijing 100083, China
  • 收稿日期:2007-01-16 修回日期:2007-02-01 出版日期:2007-09-20 发布日期:2007-09-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No~50377002).

Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem

Xie Li(谢莉)† and Lei Yin-Zhao(雷银照）   

  1. Department of Electrical Engineering, School of Automation and Electrical Engineering, Beihang University, Beijing 100083, China
  • Received:2007-01-16 Revised:2007-02-01 Online:2007-09-20 Published:2007-09-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No~50377002).

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摘要： The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

关键词: well-posedness, initial-boundary value problem, multi-medium region, Maxwell's equations

Abstract: The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday's law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

Key words: well-posedness, initial-boundary value problem, multi-medium region, Maxwell's equations

中图分类号:  (Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems)

  • 41.20.Gz
02.30.Rz (Integral equations) 02.60.Lj (Ordinary and partial differential equations; boundary value problems)