On the scattering of electromagnetic waves by perfectly conducting bodies moving in vacuum. Part 1: Formulation and reformulation of the scattering problem

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 boundry of its space-time track is smooth and can be mapped and smoothly onto a cylinder, while the speeds of points on the body must remain less than that of light in vacuum. Within this setting, uniqueness 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.