Abstract:
All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs.
Keywords:
radial motion of the gas, collapse, source, separation of variables.
Citation:
S. V. Khabirov, “Partially invariant solutions for a submodel of radial motions of a gas”, Prikl. Mekh. Tekh. Fiz., 48:5 (2007), 26–34; J. Appl. Mech. Tech. Phys., 48:5 (2007), 641–648
\Bibitem{Kha07}
\by S.~V.~Khabirov
\paper Partially invariant solutions for a submodel of radial motions of a gas
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2007
\vol 48
\issue 5
\pages 26--34
\mathnet{http://mi.mathnet.ru/pmtf2070}
\elib{https://elibrary.ru/item.asp?id=17249468}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2007
\vol 48
\issue 5
\pages 641--648
\crossref{https://doi.org/10.1007/s10808-007-0082-z}
Linking options:
https://www.mathnet.ru/eng/pmtf2070
https://www.mathnet.ru/eng/pmtf/v48/i5/p26
This publication is cited in the following 1 articles:
V. Potyakov, “Class of differentially invariant solutions of the submodel of axisymmetric flows of an ideal gas”, J. Appl. Mech. Tech. Phys., 50:8 (2009), 754–759
Citation in format AMSBIB
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