Geodesic
Generalized theory of normal waves in layered media
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 109-120
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Using the example of the Pekeris waveguide, we show that boundary value problems for a layered half-space in the classical setting are ill-posed. One of the solutions of the reduced Pekeris boundary value problem is suggested, which satisfies the generalized radiation condition on the impedance interface. The mode part of this solution is represented by the expansion in the complete system of normal waves, including regular, generalized, and leaky waves. We construct an extension of the solution to the half-space in the class of generalized functions satisfying the quenching condition at infinity. Foundations of the generalized theory are formulated. Peculiarities of the generalized theory as compared to the classical theory are analyzed.
Keywords: Pekeris boundary value problem, non-self-adjoint operator, generalized functions, model solution. 
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B. A. Kasatkin; N. V. Zlobina. Generalized theory of normal waves in layered media. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 16 (2010) no. 2, pp. 109-120. http://geodesic.mathdoc.fr/item/TIMM_2010_16_2_a7/

[1] Pekeris C. L., “Theory of propagation of explosive sound in shallow water”, Geol. Soc. Am., 27 (1948), 48–156

[2] Brekhovskikh L. M., Volny v sloistykh sredakh, Izd-vo AN SSSR, M., 1957, 502 pp. | MR

[3] Ewing W. M., Jardetzky W. S., Press F., Elastic waves in layered media, McGraw-Hill, New York, 1957, 380 pp. | MR | Zbl

[4] Lamb H., “On the propagaition of tremors over the surface on the elastic solid”, Phyl. Trans. Roy. Soc. A London, 203 (1904), 1–42 | DOI

[5] Malyuzhinets G. D., “Matematicheskaya formulirovka zadachi o vynuzhdennykh garmonicheskikh kolebaniyakh v proizvolnoi oblasti”, Dokl. AN SSSR, 78:3 (1951), 439–442 | Zbl

[6] Kasatkin B. A., Zlobina N. V., Nekorrektnye zadachi i obobschennye volny v akustike sloistykh sred, Dalnauka, Vladivostok, 2005, 407 pp.

[7] Shevchenko V. V., “Sobstvennye volny odnorodnoi ploskoi impedansnoi poverkhnosti”, Akust. zhurn., 9:2 (1967), 215–221 | MR

[8] Kasatkin B. A., Zlobina N. V., “Korrektnaya postanovka zadachi Pekerisa i obobschennaya teoriya sloistykh volnovodov”, Akustika neodnorodnykh sred. Tr. nauch. shk. prof. S. A. Rybaka, 7, Trovant, Troitsk, 2006, 121–131

[9] De Santo Dzh., “Teoreticheskie metody v akustike okeana”, Akustika okeana, ed. Dzh. De Santo, Mir, M., 1982, 16–90

[10] Kasatkin B. A., Zlobina N. V., “Ob odnom klasse anomalnykh yavlenii v akustike sloistykh sred (obzor)”, Sb. tr. XVIII sessii RAO, v. 2, GEOS, M., 2006, 217–220

[11] Kasatkin B. A., Zlobina N. V., “Sravnitelnyi analiz klassicheskogo i obobschennogo reshenii granichnoi zadachi Pekerisa”, Akustika neodnorodnykh sred. Tr. nauch. shk. prof. S. A. Rybaka, 8, Trovant, Troitsk, 2007, 158–171

[12] Kasatkin B. A. [i dr.], Printsipy postroeniya gidroakusticheskikh navigatsionnykh sistem dalnego radiusa deistviya, [Elektron. resurs]: Proceed. of the internat. conf. on Subsea technologies. Saint-Petersburg 1 CD-ROM , 2007 http://www.subseatech2007.smtu.ru.