 | | 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: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 79, Issue 4 / 2015 | Next article >> |
| S.P. Bautin and S.L. Deryabin, "Two-dimensional solutions of the shallow water equations in the neighbourhood of a shoreline," J. Appl. Math. Mech. 79 (4), 358-366 (2015) |
| Year |
2015 |
Volume |
79 |
Issue |
4 |
Pages |
358-366 |
| DOI |
10.1016/j.jappmathmech.2016.01.006 |
| Title |
Two-dimensional solutions of the shallow water equations in the neighbourhood of a shoreline |
| Author(s) |
S.P. Bautin (Ural State university of Railway Transport, Ekaterinburg, Russia, sbautin@usurt.ru)
S.L. Deryabin (Ural State university of Railway Transport, Ekaterinburg, Russia, sderyabin@usurt.ru) |
| Abstract |
Two-dimensional shallow water flows when the boundary is smooth at the initial instant of time are considered. Three different flow configurations when a wave reaches the shore: a) with a finite inclination, b) with zero inclination (a long tongue) and c) with a vertical to the shoreline (breaking of the wave) are examined. Theorems in the existence and uniqueness of the solutions of the initial-boundary value problems are proved. The solutions are constructed in the form of series that converge in the neighbourhood of the shoreline. The laws of motion of the shoreline and the instants of time up to which a continuous flow pattern is maintained and after which another flow configuration emerges are found. |
| Received |
04 December 2014 |
| Link to Fulltext |
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