Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains
Abstract
We discuss the radiation problem of total reflection for a time-harmonic generalized Maxwell system in a non-smooth exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the identity. By means of the limiting absorption principle, a Fredholm alternative holds true and the eigensolutions decay polynomially resp. exponentially at infinity. We prove that the corresponding eigenvalues do not accumulate even at zero. Next, we show the convergence of the time-harmonic solutions to a solution of an electro-magneto static Maxwell system as the frequency tends to zero. Finally we are able to generalize these results easily to the corresponding Maxwell system with inhomogeneous boundary data. This paper is thought of as the first and introductory one in a series of three papers, which will completely discuss the low frequency behavior of the solutions of the time-harmonic Maxwell equations.
Keywords
Cite
@article{arxiv.1105.4066,
title = {Low Frequency Asymptotics for Time-Harmonic Generalized Maxwell Equations in Nonsmooth Exterior Domains},
author = {Dirk Pauly},
journal= {arXiv preprint arXiv:1105.4066},
year = {2011}
}
Comments
Key Words: Maxwell's equations, exterior boundary value problems, radiating solutions, polynomial and exponential decay of eigensolutions, variable coefficients, electro-magneto static, electro-magnetic theory, low frequency asymptotics, inhomogeneous boundary data