Zobrazeno 1 - 10
of 260
pro vyhledávání: '"Andrei D. Polyanin"'
Publikováno v:
Mathematics, Vol 12, Iss 13, p 2127 (2024)
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations. An overview of the Monge–Ampè
Externí odkaz:
https://doaj.org/article/25c3ff1b85b3436e9cf2d28e562ad2ce
Publikováno v:
Mathematics, Vol 11, Iss 14, p 3111 (2023)
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 on
Externí odkaz:
https://doaj.org/article/880630027ea04959beefded904f9dbb8
Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays
Publikováno v:
Mathematics, Vol 11, Iss 3, p 516 (2023)
The study gives a brief overview of publications on exact solutions for functional PDEs with delays of various types and on methods for constructing such solutions. For the first time, second-order wave-type PDEs with a nonlinear source term containi
Externí odkaz:
https://doaj.org/article/8ed9c5354a414524aa1a0eb18bc72038
Autor:
Andrei D. Polyanin, Alexei I. Zhurov
Publikováno v:
Mathematics, Vol 10, Iss 9, p 1529 (2022)
The study considers a nonlinear multi-parameter reaction–diffusion system of two Lotka–Volterra-type equations with several delays. It treats both cases of different diffusion coefficients and identical diffusion coefficients. The study describes
Externí odkaz:
https://doaj.org/article/e563afe1a6aa420da98eb59ab8d57e77
Publikováno v:
Mathematics, Vol 9, Iss 5, p 511 (2021)
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 fre
Externí odkaz:
https://doaj.org/article/213180aac47441c4a8b93173485f3b57
Publikováno v:
Mathematics, Vol 9, Iss 4, p 345 (2021)
This paper describes a number of simple but quite effective methods for constructing exact solutions of nonlinear partial differential equations that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (
Externí odkaz:
https://doaj.org/article/899c478864364022ba750c5cd7e86794
Autor:
Andrei D. Polyanin
Publikováno v:
Mathematics, Vol 8, Iss 1, p 90 (2020)
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematic
Externí odkaz:
https://doaj.org/article/c2feba4e62f24bdb82f5d85e3bb5567b
Autor:
Andrei D. Polyanin
Publikováno v:
Mathematics, Vol 7, Iss 5, p 386 (2019)
The paper shows that, in looking for exact solutions to nonlinear PDEs, the direct method of functional separation of variables can, in certain cases, be more effective than the method of differential constraints based on the compatibility analysis o
Externí odkaz:
https://doaj.org/article/70a2663a6b214b8ab808b60ed494fcc4
Autor:
Andrei D. Polyanin, Inna K. Shingareva
Publikováno v:
Publishing Research Quarterly. 38:180-188
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::53e3d455be39ec13f60824e27ac99b52
https://doi.org/10.1007/s12109-022-09869-2
https://doi.org/10.1007/s12109-022-09869-2
Autor:
Andrei D. Polyanin
This reference book describes the exact solutions of the following types of mathematical equations:● Algebraic and Transcendental Equations ● Ordinary Differential Equations ● Systems of Ordinary Differential Equations ● First-Order Partial D
