Asymptotic behaviour of solutions of Maxwell’s equations in exterior domains

Article type: Research Article

Authors: Jochmann, Frank

Affiliations: Institut für angewandte Mathematik, Humboldt Universität Berlin, Unter den Linden 6, 10099 Berlin, Germany

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.

Keywords: Maxwell’s equations, exterior boundary‐value problem, asymptotic behaviour, completeness of the wave operators

Journal: Asymptotic Analysis, vol. 21, no. 3‐4, pp. 331-363, 1999