 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| P.Ye. Karabut and V.V. Ostapenko, "The method of successive approximations for solving the problem of the decay of a discontinuity and its application to the equations of two-layer shallow water theory," J. Appl. Math. Mech. 75 (4), 419-431 (2011) |
| Year |
2011 |
Volume |
75 |
Issue |
4 |
Pages |
419-431 |
| Title |
The method of successive approximations for solving the problem of the decay of a discontinuity and its application to the equations of two-layer shallow water theory |
| Author(s) |
P.Ye. Karabut (Novosibirsk, Russia, karabutp@mail.ru)
V.V. Ostapenko (Novosibirsk, Russia, ostapenko_vv@ngs.ru) |
| Abstract |
The method of successive approximations for solving the problem of the decay of a small amplitude discontinuity is proposed for hyperbolic systems of conservation laws. In the linear approximation, a Cauchy problem for a linear hyperbolic system is obtained. Its solution represents lines of discontinuity separating the regions in which the solution is constant. Most attention is paid to the first and second approximations, within the limits of which the discontinuities obtained in the first approximation decay into stable shock waves and rarefaction waves. An analysis of the qualitatively different flow conditions that arise when solving the problem of the failure of a dam for a two-layer shallow water model with a free boundary is presented as an example. |
| Received |
14 April 2010 |
| Link to Fulltext |
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