The problem of determining the scattered electromagnetic field produced when an initially quiescent incident field impinges upon a perfectly conducting body moving and deforming in vacuum is originally formulated as an initial-boundary-value problem for Maxwell's equations in a noncylindrical exterior domain in space-time. The motion and deformation of the scatterer are allowed to be fairly general, the essential hypotheses being that the boundary of its space-time track is smooth and can be mapped smoothly onto a cylinder, while the speeds of points on the body must remain less than that of light in vacuum.

Within this setting, uniquenes theorems are proven for various initial-boundary-value problems for a system of generalized Maxwell equations (in particular, for the scattering problem), and for the scalar wave equation, in noncylindrical domains.

A potential-theoretic approach is taken in the reformulation of the scattering problem. A boundary-integral-type representation of a sufficiently smooth solution of the scattering problem is derived, allowing the identification of "kinematic" single layer potentials appropriate for use in the reformulation. Smoothness properties and jump conditions exhibited by these potentials are examined. Proceeding from an ansatz motivated by the representation theorem and constructed from the kinematic single layer potentials, the scattering problem is reformulated in terms of two closely related systems of integrodifferential equations for unknown density functions on a cylindrical surface in space-time: if appropriate solutions of these systems exist, then the scattering problem possesses a solution which can be constructed from those solutions. A uniqueness-of-solution assertion is proven for these systems.

In the case of a stationary body which fulfills a certain global geometric condition and an incident field belonging to a specific class of very smooth functions, the corresponding simplified systems of integrodifferential equations are shown to possess solutions. The constructive existence proof employs an adaptation of the technique of successive approximations as applied by certain previous investigators in a study of initial-boundary-value problems for the scalar wave equation in a cylindrical domain. Thus, the scattering problem is solved in this special circumstance.