On Maxwell's equations in exterior domains

Abstract

In this paper the long time asymptotic behavior of solutions of Maxwell's equations with electric conductivity in an exterior domain with mixed boundary conditions is investigated. It is shown that the solution behaves asymptotically like a free space solution provided it obeys a suitable local decay-property. As a consequence the completeness of the wave-operators is obtained under very general assumptions on the coefficients. (This paper will appear in the Journal Asymptotic Analysis.)