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Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber

Margarita F. Kondratieva·Sergey Yu. Sadov
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Abstract

We put forward a conjecture about an universal asymptotical behaviour of the symbol of the Dirichlet-to-Neumann operator (considered as a pseudodifferential operator) in the 2D exterior problem for the Hemholtz equation. The conjecture is motivated by simple explicit examples and backed by numerical calculations, even in the case of a non-convex obstacle. It implies (at a physical level of rigor) Kirhhoff's approximation.

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Margarita F. Kondratieva, Sergey Yu. Sadov. 2003-10-10. Symbol of the Dirichlet-to-Neumann operator in 2D diffraction problems with large wavenumber. https://arxiv.org/abs/physics/0310048

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