 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13288 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8164
|
| In English (Mech. Solids): | | 5124 |
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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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