Abstract
A method for reducing systems of partial differential equations to corresponding systems of ordinary differential equations is proposed. 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’s equations for vacuum; and a system of gas dynamics equations in cylindrical coordinates are studied. It is shown how this approach can be used for solving certain problems (shockless compression, turbulence, etc.).
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Original Russian Text © L.I. Rubina, O.N. Ul’yanov, 2014, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Vol. 20, No. 1.
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Rubina, L.I., Ul’yanov, O.N. One method for solving systems of nonlinear partial differential equations. Proc. Steklov Inst. Math. 288 (Suppl 1), 180–188 (2015). https://doi.org/10.1134/S0081543815020182
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DOI: https://doi.org/10.1134/S0081543815020182