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Literature Cited
B. S. Pavlov and M. D. Faddeev, “On scattering by a hollow resonator with a small aperture,” J. Sov. Math.,27, No. 1 (1984).
B. S. Pavlov and I. Yu. Popov, “A model of diffraction by an infinitely narrow crack and the theory of extensions,” Vestn. Leningr. Gos. Univ., No. 19, 36–44 (1983).
I. Yu. Popov, “A crack of zero width and the Dirichlet condition,” Dokl. Akad. Nauk SSSR,294, No. 2, 330–334 (1987).
M. M. Zimnev and I. Yu. Popov, “The choice of parameters of the model of cracks of zero width,” Zh. Vychisl. Mat. Mat. Fiz.,27, No. 3, 466–470 (1987).
B. S. Pavlov and I. Yu. Popov, “Scattering by resonators with small and point apertures,” Vestn. Leningr. Gos. Univ., No. 13, 116–118 (1984).
M. Yu. Drozdov and I. Yu. Popov, “A crack of zero width and the third boundary condition,” Vestn. Leningr. Gos. Univ., Ser. 4, No. 3, 93–95 (1987).
M. D. Faddeev, “Asymptotics of the Green function of the Neumann problem near a point of the boundary,” J. Sov. Math.,30, No. 4, (1985).
V. Yu. Gotlib, “Scattering by a circular resonator with a narrow crack as a problem of perturbation theory,” Dokl. Akad. Nauk SSSR,287, No. 5, 1109–1113 (1986).
Additional information
Leningrad. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 30, No. 3, pp. 103–108, May–June, 1989.
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Popov, I.Y. Justification of the model of cracks of zero width for the Dirichlet problem. Sib Math J 30, 428–432 (1989). https://doi.org/10.1007/BF00971497
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DOI: https://doi.org/10.1007/BF00971497