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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 238–246 (Mi timm1046)  

This article is cited in 3 scientific papers (total in 3 papers)

One method for solving systems of nonlinear partial differential equations

L. I. Rubinaa, O. N. Ul'yanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin

Abstract: A method for reducing systems of partial differential equations to corresponding systems of ordinary differential equations is proposed. We study a system of equations describing two-dimensional, cylindrical, and spherical flows of a polytropic gas, a system of dimensionless Stokes equations for the dynamics of a viscous incompressible fluid, a system of Maxwell equations for vacuum, and a system of gas dynamics equations in cylindrical coordinates. We show how this approach can be used for solving certain problems (shockless compression, turbulence, etc.).

Keywords: systems of nonlinear partial differential equations, investigation method for nonlinear partial differential equations, exact solutions.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 180–188

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 04.12.2013

Citation: L. I. Rubina, O. N. Ul'yanov, “One method for solving systems of nonlinear partial differential equations”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 238–246; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 180–188

Citation in format AMSBIB
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\paper One method for solving systems of nonlinear partial differential equations
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\yr 2014
\vol 20
\issue 1
\pages 238--246
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 288
\issue , suppl. 1
\pages 180--188
\crossref{https://doi.org/10.1134/S0081543815020182}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84958237796}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rubina L.I. Ul'yanov O.N., “on Solving Certain Nonlinear Acoustics Problems”, Acoust. Phys., 61:5 (2015), 527–533  crossref  isi  elib  scopus
    2. L. I. Rubina, O. N. Ul'yanov, “On some properties of the Navier-Stokes equations”, Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 163–174  mathnet  crossref  mathscinet  isi  elib
    3. L. I. Rubina, O. N. Ulyanov, “Ob odnom podkhode k resheniyu neodnorodnykh uravnenii v chastnykh proizvodnykh”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 27:3 (2017), 355–364  mathnet  crossref  elib
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