Journal of Applied Mathematics and Mechanics (about journal) 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
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IssuesArchive of Issues2014-6pp.599-612

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I.B. Bakholdin, "Theory and classification of the reversible structures of discontinuities in hydrodynamic-type models," J. Appl. Math. Mech. 78 (6), 599-612 (2014)
Year 2014 Volume 78 Issue 6 Pages 599-612
Title Theory and classification of the reversible structures of discontinuities in hydrodynamic-type models
Author(s) I.B. Bakholdin (Moscow, Russia, ibbakh@yandex.ru)
Abstract The results of an analysis of the numerical and analytical solutions of the partial differential equations for different models of continuum mechanics and also the solutions of the ordinary differential equations of the travelling waves for these models are presented. Typical models, the basic theses of the theory of discontinuities in models of the reversible and weakly dissipative type, the classification of time-invariant structures and time-varying ordered structures are considered. The theory includes elements such as the use of averaged equations, evolutionary conditions, conditions for the complete and partial reversibility of a discontinuity, conditions for the existence of a solution in the typical case obtained using dimensional analysis of the invariant manifolds and the number of additional parameters varied and the classification of the periodic waves, solitary waves and kinks with respect to the number of free parameters.
Received 13 February 2014
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