On the low frequency asymptotics for the 2-D electromagnetic transmission problem

ANZIAM J. 47 (2006), 397-411

On the low frequency asymptotics for the 2-D electromagnetic transmission problem

C. N. Anestopoulos
National Technical University of Athens
Department of Applied Mathematics and Physics
GR-15780 Zografou Campus
Athens
Greece
kanesto@mail.ntua.gr

and

E. E. Argyropoulos
Technological Education Institute
Department of Electrical Engineering
GR-35100 Lamia
Greece
protepkste@stellad.pde.sch.gr

Abstract

We examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.

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