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Khabirov S.V. Group analysis tasks. Conservation laws. Multiphase Systems. 18 (2023) 2. 45–49 (in Russian).
2023. Vol. 18. Issue 2, Pp. 45–49
URL: http://mfs.uimech.org/mfs2023.2.007,en
DOI: 10.21662/mfs2023.2.007
Group analysis tasks. Conservation laws
Khabirov S.V.
Mavlyutov Institute of Mechanics of UFRC RAS, Ufa, Russia

Abstract

Differential equations of mechanics are derived from the laws of conservation of mass, momentum and energy. Other conservation laws can be obtained using the symmetries of these equations. Any conservation law can be derived from one using canonical operators, special cases of which are symmetry operators. The calculation of canonical conservation law operators is equivalent to a direct method of finding a divergent form of equations that are valid by virtue of the equations of mechanics. Using the example of one-dimensional equations of gas dynamics, all zero-order conservation laws are obtained by the direct method. For special equations of state, an infinite set of conservation laws have been obtained, many of which are new.

Keywords

conservation laws,
gas dynamics,
equation of state,
compatibility conditions

Article outline

Objective: to present new problems of group analysis and, using the example of equations of one-dimensional gas dynamics, to consider algorithms for solving these problems. 

Methods: methods of group analysis and differential equations.

Result: an algorithm for obtaining conservation laws of one-dimensional equations of gas dynamics is described.

References

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    DOI: 10.21662/mfs2022.1.005
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    DOI: 10.1016/j.jmaa.2006.10.078
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  5. Ovsannikov L.V. Lectures on the basics of gas dynamics. М.: IKI 2003. 336 p. (in Russian).