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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 3, Pages 135–145 (Mi sjim746)  
This article is cited in 2 scientific papers (total in 2 papers)

Integrable hydrodynamic submodels with a linear velocity field

L. Z. Urazbakhtina

Ufa State Aviation Technical University, Ufa, Russia
Full-text PDF (295 kB) Citations (2)
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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.
Received: 26.01.2012
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 1, Pages 117–126
DOI: https://doi.org/10.1134/S1990478913010110
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
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://mathscinet.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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  • https://www.mathnet.ru/eng/sjim746
  • https://www.mathnet.ru/eng/sjim/v15/i3/p135
    • This publication is cited in the following 2 articles:
    1. L. Z. Urazbakhtina, Yu. V. Yulmukhametova, “Ploskii kollaps gaza s lineinym polem skorostei”, Tr. IMM UrO RAN, 29, no. 2, 2023, 207–216  mathnet  crossref  mathscinet  elib
    2. Renata Nikonorova, Dilara Siraeva, Yulia Yulmukhametova, “New Exact Solutions with a Linear Velocity Field for the Gas Dynamics Equations for Two Types of State Equations”, Mathematics, 10:1 (2022), 123  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский журнал индустриальной математики
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    Abstract page:317
    Full-text PDF :118
    References:70
    First page:3
     
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