### Time-dependent electromagnetic waves in a cavity

The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential $\mathbf{A}$ satisfying a wave equation with initial-boundary conditions. This description through $\mathbf{A}$ is rigorously shown to give a unique solution of the problem and is the starting...