Complete Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains
arXiv:1105.4088
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.
Key Words: low frequency asymptotics, Maxwell's equations, exterior boundary value problems, variable coefficients, electro-magneto static, Hodge-Helmholtz decompositions, radiating solutions, asymptotic expansions, spherical harmonics, Hankel functions