Search Results - "Polyanin, A. D."

Review of methods for constructing exact solutions of equations of mathematical physics based on simpler solutions by Aksenov, A. V., Polyanin, A. D.

“…We present a brief review of methods based on the use of simpler solutions for constructing exact solutions of both nonlinear equations of mathematical physics…”
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Group Analysis, Reductions, and Exact Solutions of the Monge–Ampère Equation in Magnetic Hydrodynamics by Aksenov, A. V., Polyanin, A. D.

“…We study the Monge–Ampère equation with three independent variables, which occurs in electron magnetohydrodynamics. A group analysis of this strongly nonlinear…”
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Functional Separable Solutions of Two Classes of Nonlinear Mathematical Physics Equations by Polyanin, A. D., Zhurov, A. I.

“…This study describes a new modification of the method of functional separation of variables for nonlinear equations of mathematical physics. Solutions are…”
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On One Method for Constructing Exact Solutions of Nonlinear Equations of Mathematical Physics by Polyanin, A. D., Zhurov, A. I.

“…A new method for constructing exact solutions of nonlinear equations of mathematical physics is proposed. The method is based on nonlinear integral…”
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Reaction-Diffusion Models with Delay: Some Properties, Equations, Problems, and Solutions by Polyanin, A. D., Sorokin, V. G., Vyazmin, A. V.

“…The delay reaction-diffusion models used in thermal physics, chemistry, biochemistry, biology, ecology, biomedicine, and control theory were reviewed. New…”
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Transformations, properties, and exact solutions of unsteady axisymmetric boundary layer equations for non-Newtonian fluids by Polyanin, A. D., Zaitsev, V. F.

“…Unsteady axisymmetric boundary layer equations for power-law non-Newtonian fluids are analyzed. A number of new exact solutions containing arbitrary functions…”
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On order reduction of non-linear equations of mechanics and mathematical physics, new integrable equations and exact solutions by Polyanin, A.D., Zhurov, A.I.

“…Some classes of non-linear equations of mechanics and mathematical physics are described that admit order reduction through the use of a hydrodynamic-type…”
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Exact solutions of nonlinear heat- and mass-transfer equations by Polyanin, A. D., Zhurov, A. I., Vyaz’min, A. V.

“…The method of generalized separation of variables for solving nonlinear steady and unsteady heat- and mass-transfer equations is outlined. New exact solutions…”
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Exact solutions to the Navier-Stokes equations with generalized separation of variables by Polyanin, A. D.

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Exact solutions of nonlinear sets of equations of the theory of heat and mass transfer in reactive media and mathematical biology by Polyanin, A. D.

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Foams as specific gas-liquid technological media by Kazenin, D. A., Vyaz’min, A. V., Polyanin, A. D.

“…Basic physicochemical notions of foams as specific gas-liquid technological media are systematized. Structural properties, main parameters, and models of foam…”
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Transformations, properties, and exact solutions of nonstationary axisymmetric boundary-layer equations by Polyanin, A. D.

“…A nonstationary axisymmetric boundary-layer equation with a pressure gradient, which is written for the stream function, has been studied. It has been shown…”
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Exact solutions of unsteady boundary layer equations for power-law non-Newtonian fluids by Polyanin, A. D.

“…A number of new exact solutions (with the generalized and functional separation of variables) of unsteady equations of a planar and asymmetric boundary layer…”
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Exact solutions to new classes of reaction-diffusion equations containing delay and arbitrary functions by Polyanin, A. D.

“…The following one-dimensional nonlinear delay reaction-diffusion equations are considered: , where u = u ( x,t ), w = u ( x,t −τ), and τ is the delay time. New…”
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Transformations and exact solutions of unsteady-state axisymmetric boundary layer equations by Polyanin, A. D.

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Exact generalized separable solutions to nonlinear delay reaction-diffusion equations by Polyanin, A. D.

“…Exact generalized separable solutions are derived for the nonlinear delay reaction-diffusion equations , where u = u ( x, t ), w = u ( x, t − τ), and τ is the…”
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Exact solutions to differential-difference heat and mass transfer equations with a finite relaxation time by Polyanin, A. D.

“…Certain exact solutions to the linear differential-difference heat and mass transfer equations with a finite relaxation time are specified. The exact solution…”
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Transformations and exact solutions containing arbitrary functions for boundary-layer equations by Polyanin, A. D.

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Exact solutions of the Navier-Stokes equations with the linear dependence of velocity components on two space variables by Aristov, S. N., Knyazev, D. V., Polyanin, A. D.

“…A wide class of two-dimensional and three-dimensional steady-state and non-steady-state flows of a viscous incompressible fluid is considered. It is assumed…”
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Differential-difference heat-conduction and diffusion models and equations with a finite relaxation time by Polyanin, A. D., Vyazmin, A. V.

“…Differential-difference heat conduction and diffusion models and equations with a finite relaxation time are described that give a finite disturbance…”
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