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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 1, Pages 238–246 (Mi timm1046)  
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (163 kB) Citations (5)
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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.
Received: 04.12.2013
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 288, Issue 1, Pages 180–188
DOI: https://doi.org/10.1134/S0081543815020182
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
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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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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