Estimation of a 2D Fourier integral for the quarter-plane diffraction problem

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• Andrey Shanin (Moscow State University)
• Tuesday 07 February 2023, 11:45-12:30
• Seminar Room 1, Newton Institute.

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MWSW01 - Canonical scattering problems

The classical problem of diffraction of a scalar monochromatic wave by a Dirichlet thin quarter-plane screen in the 3D space is studied. As it is known, this problem admits separation of variables, but no analog of the Wiener-Hopf method for it has been built. In [1] we propose an approach enabling one to study the singularities of the solution of the problem a priori (i.e. without building the solution). The wave field becomes represented as a 2D Fourier integral whose transformant has an unknown regular part and an explicitly known singular part. Here we address a technical but important problem: we reconstruct the principal wave terms from the singularities of the Fourier transformant. As the basic technique, we use the method developed in [2]. We demonstrate that the locality principle is applicable to the integral: the principal wave terms are produced by the crossings of the singularity components or the saddle points on the singularity. After a careful analysis, we obtain that all components obtained this way correspond to certain rays. The work is co-authored by R.C.Assier and A.I.Korolkov. [1] R.C.Assier, A.V.Shanin, Diffraction by a quarter-plane. Analytical continuation of spectral function // QJMAM V . 72, 51-85 (2019). [2] R.C.Assier, A.V.Shanin, A.I.Korolkov, A contribution to the mathematical theory of diffraction: a note on double Fourier integrals // QJMAM , DOI: 10.1093/qjmam/hbac017

This talk is part of the Isaac Newton Institute Seminar Series series.

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