Well-posedness of the time-varying linear electro-magnetic initial-boundary value problem |
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| Authors: | Xie Li and Lei Yin-Zhao |
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| Affiliation: | Department of Electrical Engineering, School of Automation and Electrical Engineering, Beihang University, Beijing 100083, China |
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| 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. |
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| Keywords: | well-posedness initial-boundary value problem multi-medium region Maxwell's equations |
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