A contribution to the mathematical theory of diffraction. Part II: Recovering the far-field asymptotics of the quarter-plane problem

Авторы: Assier R.C., Shanin A.V., Korolkov A.I.
Журнал: Quarterly Journal of Mechanics and Applied Mathematics
Том: 77
Номер: 1-2
Год издания: 2024
Издательство: Oxford University Press
Местоположение издательства: United Kingdom
Первая страница: 1
Последняя страница: 32
DOI: 10.1093/qjmam/hbae005
Аннотация: We apply the stationary phase method developed in Assier, Shanin and Korolkov, QJMAM, 76(2022) to the problem of wave diffraction by a quarter-plane subjected to Dirichlet boundaryconditions. The wave field is written as a double Fourier transform of an unknown spectralfunction. We make use of the analytical continuation results of Assier and Shanin, QJMAM, 72(2018) to uncover the singularity structure of this spectral function. This allows us to provide aclosed-form far-field asymptotic expansion of the field by estimating the double Fourier integralnear some special points of the spectral function. All the known results on the far-field asymptoticsof the quarter-plane problem are recovered, and new mathematical expressions are derived for thesecondary diffracted waves in the plane of the scatterer.
Добавил в систему: Шанин Андрей Владимирович

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