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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 264, Pages 66–82
(Mi znsl1159)
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This article is cited in 54 scientific papers (total in 54 papers)
An augmented scattering matrix and an exponentially decreasing solution of elliptic boundary-value problem in the domain with cylindrical outlets
I. V. Kamotskii, S. A. Nazarov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Abstract:
Self-adjoint elliptic boundary-value problem in domain with cylindrical outlets to infinity is considered. The notion of augmented scattering matrix is introduced due to artificial radiation conditions. The properties of augmented scattering matrix are studied and the connection with classical scattering matrix is demonstrated. The central point is possibility to calculate the number of leaner independent solutions of homogeneous problem with fixed rate of decreasing at infinity by analyzing the spectrum of augmented scattering matrix. This
property is applied to problem of diffraction on periodical boundary as example.
Received: 23.12.1999
Citation:
I. V. Kamotskii, S. A. Nazarov, “An augmented scattering matrix and an exponentially decreasing solution of elliptic boundary-value problem in the domain with cylindrical outlets”, Mathematical problems in the theory of wave propagation. Part 29, Zap. Nauchn. Sem. POMI, 264, POMI, St. Petersburg, 2000, 66–82; J. Math. Sci. (New York), 111:4 (2002), 3657–3666
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https://www.mathnet.ru/eng/znsl1159 https://www.mathnet.ru/eng/znsl/v264/p66
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