The electromagnetic initial boundary value problem in a domain with a chiral filling

The problem of the excitation of electromagnetic oscillations by given charge and current distributions in a domain with a nonhomogeneous chiral filling is investigated. The domain where the problem is considered may be both a finite one bounded by an ideally conducting surface and an infinite supplement to an ideally conducting bounded object. The initial boundary value problem is shown to arise, for which the generalized formulation in a special functional space is given. The existence of a unique weak solution to the problem is proven using the Galerkin method.