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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio

IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2017: 0.23

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Volume 18, Issue 1


Electromagnetic scattering by cylindrical orthotropic waveguide irises

Luis P. Castro / Roland Duduchava / David Kapanadze
Published Online: 2011-04-06 | DOI: https://doi.org/10.1515/gmj.2011.0009


The paper is devoted to the mathematical analysis of scattered time-harmonic electromagnetic waves by an infinitely long cylindrical orthotropic waveguide iris. This is modeled by an orthotropic Maxwell system in a cylindrical waveguide iris for plane waves propagating in the x 3-direction, imbedded in an isotropic infinite medium. The problem is equivalently reduced to a 2-dimensional boundary-contact problem with the operator div M grad+k 2 inside the domain and the (Helmholtz) operator Δ+k 2 = div grad+k 2 outside the domain. Here M is a 2 × 2 positive definite, symmetric matrix with constant, real valued entries. The unique solvability of the appropriate boundary value problems is proved and the regularity of solutions is established in Bessel potential spaces.

Keywords.: Maxwell's system; orthotropic waveguide; Helmholtz's equation; uniqueness; existence; potential theory; boundary pseudodifferential equation

About the article

Received: 2009-11-02

Published Online: 2011-04-06

Published in Print: 2011-03-01

Citation Information: Georgian Mathematical Journal, Volume 18, Issue 1, Pages 99–120, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2011.0009.

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