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 $𝐀$ satisfying a wave equation with initial-boundary conditions. This description through $𝐀$ is rigorously shown to give a unique solution of the problem and is the starting...