269 research outputs found
Continuous and discrete transformations of a one-dimensional porous medium equation
We consider the one-dimensional porous medium equation . We derive point transformations of a general
class that map this equation into itself or into equations of a similar class.
In some cases this porous medium equation is connected with well known
equations. With the introduction of a new dependent variable this partial
differential equation can be equivalently written as a system of two equations.
Point transformations are also sought for this auxiliary system. It turns out
that in addition to the continuous point transformations that may be derived by
Lie's method, a number of discrete transformations are obtained. In some cases
the point transformations which are presented here for the single equation and
for the auxiliary system form cyclic groups of finite order
On the group classification of variable-coefficient nonlinear diffusion–convection equations
AbstractWe consider the variable coefficient diffusion–convection equation of the form f(x)ut=[g(x)D(u)ux]x+h(x)K(u)ux which has considerable interest in mathematical physics, biology and chemistry. We present a complete group classification for this class of equations. Also we derive equivalence transformations between equations that admit Lie symmetries. Furthermore, we obtain mappings that connect variable and constant coefficient equations. Exact solutions of special forms of this equations are constructed using Lie symmetries and equivalence transformations
Group Analysis of Nonlinear Fin Equations
Group classification of a class of nonlinear fin equations is carried out
exhaustively. Additional equivalence transformations and conditional
equivalence groups are also found. They allow to simplify results of
classification and further applications of them. The derived Lie symmetries are
used to construct exact solutions of truly nonlinear equations for the class
under consideration. Nonclassical symmetries of the fin equations are
discussed. Adduced results amend and essentially generalize recent works on the
subject [M. Pakdemirli and A.Z. Sahin, Appl. Math. Lett., 2006, V.19, 378-384;
A.H. Bokhari, A.H. Kara and F.D. Zaman, Appl. Math. Lett., 2006, V.19,
1356-1340].Comment: 6 page
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