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.
Received: 16 January 2007
Revised: 01 February 2007
Accepted manuscript online:
PACS:
41.20.Gz
(Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems)
(Ordinary and partial differential equations; boundary value problems)
Fund: Project supported by the
National Natural Science Foundation of China (Grant No~50377002).
Cite this article:
Xie Li(谢莉) and Lei Yin-Zhao(雷银照） Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem 2007 Chinese Physics 16 2523
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