Abstract:
The group analysis of differential equations of ideal gas dynamics is most developed. Earlier, the state equations for thermodynamic parameters were assumed to be time-independent. The time dependence may take place for relaxing media, for example, as a result of rheology or due to the energy averaging of processes in a multiphase medium. The problem of group analysis of relaxing media is posed. First, equivalence transformations are calculated that change only the state equations. Next, the problem of group classification is solved: it is required to find, up to equivalence transformations, classes of state equations for which the admitted group is extended. This problem is partially solved in the present paper.
Keywords:
gas dynamics, relaxing state equations, equivalence transformations, group classification.
Citation:
S. V. Khabirov, “On the Group Classification of Ideal Gas-Dynamic Relaxing Media”, Trudy Inst. Mat. i Mekh. UrO RAN, 29, no. 2, 2023, 260–270; Proc. Steklov Inst. Math. (Suppl.), 321, suppl. 1 (2023), S127–S137
\Bibitem{Kha23}
\by S.~V.~Khabirov
\paper On the Group Classification of Ideal Gas-Dynamic Relaxing Media
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2023
\vol 29
\issue 2
\pages 260--270
\mathnet{http://mi.mathnet.ru/timm2012}
\crossref{https://doi.org/10.21538/0134-4889-2023-29-2-260-270}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4610505}
\elib{https://elibrary.ru/item.asp?id=53846822}
\edn{https://elibrary.ru/rizngy}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2023
\vol 321
\issue , suppl. 1
\pages S127--S137
\crossref{https://doi.org/10.1134/S0081543823030124}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85171375056}
Linking options:
https://www.mathnet.ru/eng/timm2012
https://www.mathnet.ru/eng/timm/v29/i2/p260
This publication is cited in the following 1 articles:
S. V. Khabirov, “Group Classification of Ideal Gas-Dynamic Relaxing Media by the Method of an Optimal System of Subalgebras”, Sib Math J, 66:1 (2025), 95
Citation in format AMSBIB
Contact us: