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**Thin-layer solutions of the Helmholtz equation.**
*(English)*
Zbl 1478.78070

Summary: 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.

### MSC:

78M35 | Asymptotic analysis in optics and electromagnetic theory |

78A05 | Geometric optics |

78A45 | Diffraction, scattering |

78A40 | Waves and radiation in optics and electromagnetic theory |

35J05 | Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation |

35K10 | Second-order parabolic equations |

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\textit{J. R. Ockendon} and \textit{R. H. Tew}, Eur. J. Appl. Math. 32, No. 5, 769--783 (2021; Zbl 1478.78070)

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### References:

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