Scattering of Electromagnetic Waves by Perfectly Conducting Bodies Moving in Vacuum. Part 1. Formulation and Reformulation of the Scattering Problem

摘要

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.