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Sib. Zh. Ind. Mat., 2012, Volume 15, Number 3, Pages 135–145 (Mi sjim746)  

Integrable hydrodynamic submodels with a linear velocity field

L. Z. Urazbakhtina

Ufa State Aviation Technical University, Ufa, Russia

Abstract: Invariant and partially invariant solutions to equations of gas dynamics with a linear velocity field are given by a matrix satisfying a homogeneous integrable Riccati equation. The classification of solutions by the acceleration vector in the Lagrangian coordinates is carried out. We give an example of an invariant solution for which the selected volume “collapses” to an interval.

Keywords: gas dynamics equations, state equation, intregrable submodels with linear velocity field.

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English version:
Journal of Applied and Industrial Mathematics, 2013, 7:1, 117–126

Bibliographic databases:

UDC: 517.958
Received: 26.01.2012

Citation: L. Z. Urazbakhtina, “Integrable hydrodynamic submodels with a linear velocity field”, Sib. Zh. Ind. Mat., 15:3 (2012), 135–145; J. Appl. Industr. Math., 7:1 (2013), 117–126

Citation in format AMSBIB
\Bibitem{Ura12}
\by L.~Z.~Urazbakhtina
\paper Integrable hydrodynamic submodels with a~linear velocity field
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 3
\pages 135--145
\mathnet{http://mi.mathnet.ru/sjim746}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3098814}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 1
\pages 117--126
\crossref{https://doi.org/10.1134/S1990478913010110}


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