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IssuesArchive of Issues2011-4pp.419-431

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
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 http://www.sciencedirect.com/science/journal/00218928
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