[图书][B] Nonlinear reaction-diffusion-convection equations: Lie and conditional symmetry, exact solutions and their applications
R Cherniha, M Serov, O Pliukhin - 2017 - taylorfrancis.com
It is well known that symmetry-based methods are very powerful tools for investigating
nonlinear partial differential equations (PDEs), notably for their reduction to those of lower …
nonlinear partial differential equations (PDEs), notably for their reduction to those of lower …
Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source
A new approach to group classification problems and more general investigations on
transformational properties of classes of differential equations is proposed. It is based on …
transformational properties of classes of differential equations is proposed. It is based on …
Symmetry reduction and exact solutions of the Navier-Stokes equations. I
W Fushchych, R Popowych - Journal of nonlinear mathematical physics, 1994 - Springer
Abstract Ansatzes for the Navier-Stokes field are described. These ansatzes reduce the
Navier-Stokes equations to system of differential equations in three, two, and one …
Navier-Stokes equations to system of differential equations in three, two, and one …
Conservation laws and potential symmetries of linear parabolic equations
We carry out an extensive investigation of conservation laws and potential symmetries for
the class of linear (1+ 1)-dimensional second-order parabolic equations. The group …
the class of linear (1+ 1)-dimensional second-order parabolic equations. The group …
Conditional symmetry of a porous medium equation
RZ Zhdanov, VI Lahno - Physica D: Nonlinear Phenomena, 1998 - Elsevier
We obtain an exhaustive description of conditional symmetries admitted by a nonlinear
porous medium equation in one spatial dimension. It is proved that solving the determining …
porous medium equation in one spatial dimension. It is proved that solving the determining …
Point and generalized symmetries of the heat equation revisited
SD Koval, RO Popovych - Journal of Mathematical Analysis and …, 2023 - Elsevier
We derive a nice representation for point symmetry transformations of the (1+ 1)-
dimensional linear heat equation and properly interpret them. This allows us to prove that …
dimensional linear heat equation and properly interpret them. This allows us to prove that …
[HTML][HTML] New conditional symmetries and exact solutions of reaction–diffusion–convection equations with exponential nonlinearities
R Cherniha, O Pliukhin - Journal of Mathematical Analysis and Applications, 2013 - Elsevier
A complete description of Q-conditional symmetries for a class of reaction–diffusion–
convection equations with exponential diffusivities is derived. It is shown that all the known …
convection equations with exponential diffusivities is derived. It is shown that all the known …
[HTML][HTML] Group classification of linear evolution equations
A Bihlo, RO Popovych - Journal of mathematical analysis and applications, 2017 - Elsevier
The group classification problem for the class of (1+ 1)-dimensional linear rth order evolution
equations is solved for arbitrary values of r> 2. It is shown that a related maximally gauged …
equations is solved for arbitrary values of r> 2. It is shown that a related maximally gauged …
Exact solutions of diffusion-convection equations
NM Ivanova - arXiv preprint arXiv:0710.4000, 2007 - arxiv.org
arXiv:0710.4000v3 [math-ph] 7 Aug 2008 Page 1 arXiv:0710.4000v3 [math-ph] 7 Aug 2008
Exact Solutions of Diffusion–Convection Equations Nataliya M. Ivanova Institute of …
Exact Solutions of Diffusion–Convection Equations Nataliya M. Ivanova Institute of …
Potential nonclassical symmetries and solutions of fast diffusion equation
The fast diffusion equation [Formula: see text] is investigated from the symmetry point of view
in development of the paper by Gandarias [ML Gandarias, Phys. Lett. A 286 (2001) 153] …
in development of the paper by Gandarias [ML Gandarias, Phys. Lett. A 286 (2001) 153] …