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

The well-posedness of the initial-boundary value problem of the time-varyinglinear electromagnetic field in a multi-medium region is investigated.Function spaces are defined, with Faraday's law ofelectromagnetic induction and the initial-boundary conditions consideredas constraints. Gauss's formula applied to a multi-medium region is used to derive the energy-estimatinginequality. After converting the initial-boundary conditions intohomogeneous ones and analysing the characteristics of an operator introducedaccording to the total current law, the existence, uniqueness and stabilityof the weak solution to the initial-boundary value problem ofthe time-varying linear electromagnetic field are proved.