Complete low frequency asymptotics for time-harmonic generalized Maxwell equations in nonsmooth exterior domains

Article type: Research Article

Authors: Pauly, Dirk

Affiliations: Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, Universitätsstr. 2, 45117 Essen, Germany. E-mail: dirk.pauly@uni-due.de

Abstract: We continue the study of the operator of generalized Maxwell equations and completely discover the behavior of the solutions of the time-harmonic equations as the frequency tends to zero. Thereby we identify degenerate operators in terms of special ‘polynomially growing’ solutions of a corresponding static problem, which must be added to the ‘usual’ Neumann series in order to describe the low frequency asymptotic adequately.

Keywords: low frequency asymptotics, exterior boundary value problems, Maxwell's equations, variable coefficients, electro-magneto static, Hodge–Helmholtz decompositions, radiating solutions, asymptotic expansions, spherical harmonics, Hankel functions

DOI: 10.3233/ASY-2008-0898

Journal: Asymptotic Analysis, vol. 60, no. 3-4, pp. 125-184, 2008