Κατεύθυνση Εφαρμοσμένα Μαθηματικά
Library of the School of Science

2012-08-20

2012

Γιακουστίδη Αλεξάνδρα

Αθανασιάδης Χριστόδουλος Καθηγητής (Επιβλέπων), Κόττα--Αθανασιάδου Ευαγγελία Λέκτορας, Σεβρόγλου Βασίλειος

Προβλήματα Συνοριακών Τιμών για το σύστημα Maxwell με αρμονική χρονική εξάρτηση

Greek

Our study is about the scattering of time-harmonic waves by obstacles
surrounded by a homogeneous medium with vanishing conductivity. We consider the
Maxwell’s equations for time-harmonic electromagnetic waves. The physical
parameters of the media are introduced via the constitutive relations. We state
the boundary conditions for a perfectly conducting body and the dielectric. The
scattered field satisfies the Silver-Muller radiation condition, that is, the
scattered wave vanishes to infinity. We state and prove theorems for the
integral representations of the exterior and the interior vector fields. By
eliminating either the electric or the magnetic vector field in Maxwell’s
equations, we are led to the modified vector Helmholtz equation for the
remaining field. We state boundary value problems for the above mentioned
equation and we study thoroughly the uniqueness and existence of their
solutions. Next we study electromagnetic wave scattering by a scatterer that is
not perfectly conducting but that does not allow electromagnetic waves to
penetrate deeply into the obstacle. This problem is modeled by an impedance
boundary condition. Moreover, boundary conditions for the dielectric are stated
and the uniqueness of the scatterer field is defined by the far-field pattern.
We also study uniqueness and existence of problems with mixed boundary
conditions. Finally, we introduce the notion of vector potentials. We apply
Gauss theorem for the surface divergence for which independent coordinates are
also defined.

Electromagnetic scattering, Integral representations, Boundary value problems, Existence and uniqueness, Single and double vector potentials

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https://pergamos.lib.uoa.gr/uoa/dl/object/1319528