Frank Jochmann
On Maxwell's equations in exterior domains
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976)

MSC:

 35Q60 Equations of electromagnetic theory and optics

78A35 Motion of charged particles

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.)
Keywords: Maxwell's equations, exterior boundary value problem, asymptotic behavior