Proceedings of the Steklov Institute of Mathematics, volume 261, issue S1, pages 183-200

On solving the potential equation

Publication type: Journal Article
Publication date: 2008-07-01
scimago Q3
wos Q4
SJR: 0.289
CiteScore: 0.9
Impact factor: 0.4
ISSN: 00815438, 15318605
Mathematics (miscellaneous)
Abstract
We consider planar nonstationary potential flows of polytropic gas. The corresponding partial differential equation is studied by the method of level surfaces. Sufficient conditions on the arbitrary functions providing the construction of exact solutions of the potential equation are obtained. Equations for shock waves separating the potential flow from the rest area or from the area of motion with constant velocity are written out.
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Pleiades Publishing
On some properties of the Navier–Stokes system of equations
Rubina L.I., Ul’yanov O.N.
Proceedings of the Steklov Institute of Mathematics scimago Q3 wos Q4 , 
2017-07-01,  citations by CoLab: 0 ,  Abstract  
We discuss the initial and boundary value problems for the system of dimensionless Navier–Stokes equations describing the dynamics of a viscous incompressible fluid using the method of characteristics and the geometric method developed by the authors. Some properties of the formulation of these problems are considered. We study the effect of the Reynolds number on the flow of a viscous fluid near the surface of a body.
Pleiades Publishing
On solving certain nonlinear acoustics problems
Rubina L.I., Ul’yanov O.N.
Acoustical Physics scimago Q3 wos Q4 , 
2015-09-12,  citations by CoLab: 2 ,  Abstract  
Previously the authors developed a geometric method for studying and solving nonlinear equations and systems of equations with partial derivatives. This method is used in this paper to obtain a series of exact solutions to certain nonlinear acoustics equations, as well as to reduce the system of Euler equations to systems of common differential equations.
Pleiades Publishing
One method for solving systems of nonlinear partial differential equations
Rubina L.I., Ul’yanov O.N.
Proceedings of the Steklov Institute of Mathematics scimago Q3 wos Q4 , 
2015-04-15,  citations by CoLab: 2 ,  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.).
Pleiades Publishing
On some method for solving a nonlinear heat equation
Rubina L.I., Ul’yanov O.N.
Siberian Mathematical Journal scimago Q2 wos Q2 , 
2012-09-01,  citations by CoLab: 6 ,  Abstract  
Some exact solutions to a nonlinear heat equation are constructed. An initial-boundary value problem is examined for a nonlinear heat equation. To construct solutions, the problem for a partial differential equation of the second order is reduced to a similar problem for a first order partial differential equation.

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Proceedings of the Steklov Institute of Mathematics
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Siberian Mathematical Journal
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