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Thin-layer solutions of the Helmholtz equation

Part of: Optics, electromagnetic theory - Basic methods Optics, electromagnetic theory - General

Published online by Cambridge University Press:  06 October 2020

J. R. OCKENDON Open the ORCID record for J. R. OCKENDON [Opens in a new window]  and
R. H. TEW
J. R. OCKENDON
Affiliation:
Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK email: ock@maths.ox.ac.uk
R. H. TEW
Affiliation:
School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK email: richard.tew@nottingham.ac.uk
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Abstract

This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

Keywords

Helmholtz equationhigh-frequency asymptoticsthin layersinflection points

MSC classification

Primary: 78M35: Asymptotic analysis 78A05: Geometric optics 78A45: Diffraction, scattering
Type
Papers
Information
European Journal of Applied Mathematics , Volume 32 , Special Issue 5: 30th Anniversary Special Issue , October 2021 , pp. 769 - 783
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Copyright
© The Author(s), 2020. Published by Cambridge University Press

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