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Complete Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains
Dirk Pauly
Asymptotic Analysis, 60 (3-4), (2008), 125-184
arXiv: 1105.4088v1 (math.AP)
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
License: NONEXCLUSIVE-DISTRIB 1.0
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.
Submitted to arXiv on 20 May. 2011