Invariant subspaces and conditional Lie-Bäcklund symmetries of inhomogeneous nonlinear diffusion equations

Abstract

The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and conditional Lie-Backlund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher-order conditional Lie-Backlund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical systems.