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A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2001-1pp.11-15

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A. V. Aksenov, "Linear differential relations between solutions of the equations of Euler-Poisson-Darboux class," Mech. Solids. 36 (1), 11-15 (2001)
Year 2001 Volume 36 Number 1 Pages 11-15
Title Linear differential relations between solutions of the equations of Euler-Poisson-Darboux class
Author(s) A. V. Aksenov (Moscow)
Abstract We consider elliptic equations of Euler-Poisson-Darboux type and obtain all first order linear differential relations between their solutions. The 3D Laplace equation is reduced to the Euler-Poisson-Darboux equation. It is shown that the relations obtained can be found on the basis of the symmetries of the 3D Laplace equation.
References
1.  I. N. Vekua, New Methods of Solution of Elliptic Equations [in Russian], Gostekhizdat, Moscow, Leningrad, 1948.
2.  R. Mises, Mathematical Theory of Compressible Flows [Russian translation], Izd-vo Inostr. Lit-ry, Moscow, 1961.
3.  G. V. Dzhaiani, Solution of Some problems for a Degenerate Elliptic Equation and Their Applications to Prismatic Shells [in Russian], Izd-vo Tbilisskogo Un-ta, Tbilisi, 1982.
4.  V. K. Zhdanov and B. A. Trubnikov, Quasi-gas Unstable Media [in Russian], Nauka, Moscow, 1990.
5.  A. A. Il'yushin, Continuum Mechanics [in Russian], Izd-vo MGU, Moscow, 1990.
6.  A. Weinstein, "Discontinuous integrals and generalized potential theory," Trans. Amer. Math. Soc., Vol. 63, No. 2, pp. 342-354, 1948.
7.  A. Weinstein, "The singular solutions and the Cauchy problem for generalized Tricomi equations," Comm. Pure Appl. Math., Vol. 7, No. 1, pp. 105-116, 1954.
8.  N. Kh. Ibragimov, Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow, 1983.
9.  A. V. Aksenov, "Periodic invariant solutions of equations of absolutely unstable media," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 14-20, 1997.
Received 25 October 2000
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