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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) 2018: 0.27

Online
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1572-9176
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Volume 18, Issue 3

Issues

The Robin problem for the Helmholtz equation in a starlike planar domain

Diego Caratelli
  • International Research Centre for Telecommunications and Radar, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands.
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/ Johan Gielis
  • Department Biosciences Engineering, University of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium.
  • Simon Stevin Institute for Geometry, Mina Krusemanweg 1, 5032 ME Tilburg, The Netherlands.
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/ Pierpaolo Natalini
  • Dipartimento di Matematica, Università degli Studi di Roma Tre, Largo San Leonardo Murialdo 1, 00146 Roma, Italy.
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/ Paolo Emilio Ricci
  • Dipartimento di Matematica “Guido Castelnuovo”, Università degli Studi di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy.
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/ Ilia Tavkhelidze
  • I. Vekua Institute of Applied Mathematics, I. Javakhishvili Tbilisi State University, 2 University Str., Tbilisi 0186, Georgia.
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Published Online: 2011-07-14 | DOI: https://doi.org/10.1515/gmj.2011.0031

Abstract

The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called “superformula” introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.

Keywords.: Robin problem; Helmholtz equation; starlike domain; Fourier series

About the article

Received: 2010-03-16

Revised: 2010-06-07

Published Online: 2011-07-14

Published in Print: 2011-09-01


Citation Information: Georgian Mathematical Journal, Volume 18, Issue 3, Pages 465–479, ISSN (Online) 1072-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj.2011.0031.

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