Abstract:
Exact solutions of the Kármán–Guderley equation that describes spatial gas flows in the transonic approximation are considered. A group stratification of the equation with respect to the infinite-dimensional part of the admissible group is constructed. New invariant and partly invariant solutions are obtained. The possibility of existence of solutions continuous in the entire space is analyzed for invariant submodels with one independent variable. A solution of the Kármán–Guderley equation of the double-wave type is constructed.
Keywords:
transonic flow, invariant solutions, double waves, group stratification.
Citation:
S. V. Golovin, “Group stratification and exact solutions of the equation of transonic gas motions”, Prikl. Mekh. Tekh. Fiz., 44:3 (2003), 51–63; J. Appl. Mech. Tech. Phys., 44:3 (2003), 344–354
\Bibitem{Gol03}
\by S.~V.~Golovin
\paper Group stratification and exact solutions of the equation of transonic gas motions
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2003
\vol 44
\issue 3
\pages 51--63
\mathnet{http://mi.mathnet.ru/pmtf2498}
\elib{https://elibrary.ru/item.asp?id=17274790}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2003
\vol 44
\issue 3
\pages 344--354
\crossref{https://doi.org/10.1023/A:1023429106284}
Linking options:
https://www.mathnet.ru/eng/pmtf2498
https://www.mathnet.ru/eng/pmtf/v44/i3/p51
This publication is cited in the following 4 articles:
E. I. Kaptsov, S. V. Meleshko, “Symmetry Analysis of the Two‐Dimensional Stationary Magnetogasdynamics Equations With Coriolis Force in Lagrangian Coordinates”, Stud Appl Math, 154:1 (2025)
Sergey V. Meleshko, Evgeniy I. Kaptsov, “Symmetry Analysis of the Two-Dimensional Stationary Gas Dynamics Equations in Lagrangian Coordinates”, Mathematics, 12:6 (2024), 879
E. I. Kaptsov, “Group foliations of the β-plane barotropic vorticity equation”, Journal of Mathematical Physics, 65:8 (2024)
A. A. Talyshev, “On differential-invariant solutions”, J. Math. Sci., 230:1 (2018), 167–174
Citation in format AMSBIB
Contact us: