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

• 来源期刊: 中国物理（英文版）
• 关键词: well-posedness initial-boundary value problem multi-medium region,Maxwell's equations
• 年，卷（期）: 2007,（9）
• 页码范围: 2523-2536
• 页数: 14页
• 语种: 英文

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.