Time-harmonic solutions of some dissipative problems for Maxwell's equations in a three-dimensional half space (Q1105788)

Time-harmonic solutions of some dissipative problems for Maxwell's equations in a three-dimensional half space are constructed via the principle of limiting absorption which is rigorously justified. The asymptotic behavior of the solutions so constructed for large spatial distances is then determined. This provides the means of specifying uniqueness classes for them (``radiation conditions''). Uniqueness is proved even when surface waves decaying only like \(| x| ^{- 1/2}\) along the boundary (as opposed to spatial waves decaying like \(| x| ^{-1})\) are present. Since time-harmonic solutions are, strictly speaking, physically meaningless, the sense in which the solutions so constructed are approximations for large time to the actual time-dependent solutions is established (the principle of limiting amplitude). Finally, the connection of the present approach with the time-honored Ansatz approach for a point source (e.g., a radiating dipole) is set forth.