REFERENCES
Weinstein, A., Trans. Amer. Math. Soc., 1948, vol. 63, no.2, pp. 342–354.
Weinstein, A., Comm. Pure Appl. Math., 1954, vol. 7, no.1, pp. 105–116.
Beltrami, E., Mem. R. Accad. Sci. Bologna, 1880, vol. 2, pp. 461–505 (Opere mat., 1911, vol. 3, pp. 349–382).
Euler, L., Institutiones calculi integralis, vol. 3, Petropoli, 1770, pt. 2, chaps. 3, 4, 5 (Opera Omnia, Leipzig, 1914, ser. 1, vol. 13, pp. 212–230).
Poisson, S.D., J. de L’Ecole Polytechnique, 1823, ser. 1, vol. 19, pp. 215–248.
Riemann, B., in Sochineniya (Works), Moscow, 1948, pp. 376–395.
Darboux, G., Lecons sur la theorie generale des surfaces et les applications geometriques du calcul infinitesimal, Paris, 2 ed., 1915 (1 ed., 1888), vol. 1.
Von Mises, R., Mathematical Theory of Compressible Fluid Flow, New York: Academic, 1958. Translated under the title Matematicheskaya teoriya techenii szhimaemoi zhidkosti, Moscow: Inostrannaya Literatura, 1961.
Tsaldastani, O., in Problemy mekhaniki (Problems of Mechanics), von Mises, R. and von Karman, T., Eds., Moscow, 1955, pp. 519–552.
Aksenov, A.V., Izv. RAN. Mekhanika Tverdogo Tela, 1997, no. 2, pp. 14–20.
Vekua, I.N., Novye metody resheniya ellipticheskikh uravnenii (New Methods for Solving Elliptic Equations), Moscow, 1948.
Dzhaiani, G.V., Reshenie nekotorykh zadach dlya odnogo vyrozhdayushchego ellipticheskogo uravneniya i ikh prilozheniya k prizmaticheskim obolochkam (Solution of Some Problems for a Degenerate Elliptic Equation and Their Applications to Prismatic Shells), Tbilisi, 1982.
Dzhaiani, G.V., Uravnenie Eilera-Puassona-Darbu (The Euler-Poisson-Darboux Equation), Tbilisi, 1984.
Courant, R. and Friedrichs, K., Supersonic Flow and Shock Waves, New York, 1948. Translated under the title Sverkhzvukovoe techenie i udarnye volny, Moscow: Inostrannaya Literatura, 1950.
Solyanik-Krassa, K.V., Kruchenie valov peremennogo secheniya (Torsion of Shafts of Variable Cross-Section), Moscow, 1949.
Solyanik-Krassa, K.V., Osesimmetrichnaya zadacha teorii uprugosti (The Axisymmetric Elasticity Problem), Moscow, 1987.
Weinstein, A., in Prilozheniya teorii funktsii v mekhanike sploshnykh sred, Trudy Mezhdunar. simp. T. 2. Mekhanika zhidkosti i gaza, matematicheskie metody (Applications of Function Theory in Continuum Mechanics. Proc. Int. Symp. Vol. 2: Liquid Mechanics, Mathematical Methods), Moscow, 1965.
Zhdanov, V.K. and Trudbnikov, B.A., Kvazigazovye neustoichivye sredy (Quasi-Gas Unstable Media), Moscow, 1991.
Olevskii, M.N., Dokl. Akad. Nauk SSSR, 1949, vol. 64, no.6, pp. 767–770.
Aksenov, A.V., Dokl. RAN, 2001, vol. 381, no.2, pp. 176–179.
Ibragimov, N.Kh., Gruppy preobrazovanii v matematicheskoi fizike (Transformation Groups in Mathematical Physics), Moscow, 1983.
Abramowitz, M. and Stegun, I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Washington: U.S. Government Printing Office, 1964. Translated under the title Spravochnik po spetsial’nym funktsiyam, Moscow: Nauka, 1979.
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Translated from Differentsial’nye Uravneniya, Vol. 41, No. 6, 2005, pp. 787–794.
Original Russian Text Copyright © 2005 by Aksenov.
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Aksenov, A.V. Linear Differential Relations Between Solutions of a Class of Euler-Poisson-Darboux Equations. Diff Equat 41, 824–832 (2005). https://doi.org/10.1007/s10625-005-0221-3
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DOI: https://doi.org/10.1007/s10625-005-0221-3