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18 results on '"Sorokin, Vsevolod G."'

6. Exact Solutions and Reductions of Nonlinear Diffusion PDEs of Pantograph Type

Author

Polyanin, Andrei D. and Sorokin, Vsevolod G.

Subjects
Nonlinear Sciences - Exactly Solvable and Integrable Systems, Mathematical Physics, Mathematics - Analysis of PDEs
Abstract

We study nonlinear pantograph-type reaction-diffusion PDEs, which, in addition to the unknown $u=u(x,t)$, also contain the same functions with dilated or contracted arguments of the form $w=u(px,t)$, $w=u(x,qt)$, and $w=u(px,qt)$, where $p$ and $q$ are the free scaling parameters (for equations with proportional delay we have $0

Published
2021

12. Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay.

Author

Polyanin, Andrei D. and Sorokin, Vsevolod G.

Subjects
*REACTION-diffusion equations, *NONLINEAR equations, *COMPLEX variables
Abstract

This study is devoted to reaction–diffusion equations with spatially anisotropic time delay. Reaction–diffusion PDEs with either constant or variable transfer coefficients are considered. Nonlinear equations of a fairly general form containing one, two, or more arbitrary functions and free parameters are analyzed. For the first time, reductions and exact solutions for such complex delay PDEs are constructed. Additive, multiplicative, generalized, and functional separable solutions and some other exact solutions are presented. In addition to reaction–diffusion equations, wave-type PDEs with spatially anisotropic time delay are considered. Overall, more than twenty new exact solutions to reaction–diffusion and wave-type equations with anisotropic time delay are found. The described nonlinear delay PDEs and their solutions can be used to formulate test problems applicable to the verification of approximate analytical and numerical methods for solving complex PDEs with variable delay. [ABSTRACT FROM AUTHOR]

Published
2023
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17. The heat and mass transfer modeling with time delay

Author

Sorokin, Vsevolod G, Vyazmin, Andrey V, Zhurov, Alexei I, Reznik, Vyacheslav V, and Polyanin, Andrei D

Subjects
QA
Abstract

Nonlinear hyperbolic reaction-diffusion equations with a delay in time are investigated. All equations considered here contain one arbitrary function. Exact solutions are also presented for more complex nonlinear equations in which delay arbitrarily depends on time. Exact solutions with a generalized separation of variables are found. For special cases, new exact solutions in the form of a traveling waves are obtained, some of which can be represented in terms of elementary functions. All of these solutions contain free (arbitrary) parameters, so that one can use them to solve modeling problems of heat and mass transfer with relaxation phenomena.

Published
2017

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