A symmetry analysis of some classes of evolutionary nonlinear (2+ 1)-diffusion equations with variable diffusivity
Nonlinear Dynamics, 2010•Springer
Abstract In this paper the (2+ 1)-nonlinear diffusion equation ut− div (f (u) grad u)= 0 with
variable diffusivity is considered. Using the Lie method, a complete symmetry classification
of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the
equation, to first-or second-order ordinary differential equations are given. In a few
interesting cases exact solutions are presented.
variable diffusivity is considered. Using the Lie method, a complete symmetry classification
of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the
equation, to first-or second-order ordinary differential equations are given. In a few
interesting cases exact solutions are presented.
Abstract
In this paper the (2+1)-nonlinear diffusion equation u t −div(f(u)grad u)=0 with variable diffusivity is considered. Using the Lie method, a complete symmetry classification of the equation is presented. Reductions, via two-dimensional Lie subalgebras of the equation, to first- or second-order ordinary differential equations are given. In a few interesting cases exact solutions are presented.
Springer
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